Parcial final series de tiempo

Jeffry Jerena y David Lizcano

import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from tabulate import tabulate

EDA

# Ruta del archivo CSV
BHdata = "C:\\Users\\Maestriadatos\\Documents\\lizcanollerenaparcial\\docs\\bitcoinhistoricaldata.csv"

# Cargar los datos
df = pd.read_csv(BHdata)

# Mostrar los primeros 5 registros para visualizar los datos
print("Primeros 5 registros:")
print(df.head())

# Mostrar la información de los tipos de datos
print("\nTipos de datos por columna:")
print(df.dtypes)

Primeros 5 registros:
         Date     Price      Open      High       Low     Vol. Change %
0  03/24/2024  67,211.9  64,036.5  67,587.8  63,812.9   65.59K    4.96%
1  03/23/2024  64,037.8  63,785.6  65,972.4  63,074.9   35.11K    0.40%
2  03/22/2024  63,785.5  65,501.5  66,633.3  62,328.3   72.43K   -2.62%
3  03/21/2024  65,503.8  67,860.0  68,161.7  64,616.1   75.26K   -3.46%
4  03/20/2024  67,854.0  62,046.8  68,029.5  60,850.9  133.53K    9.35%

Tipos de datos por columna:
Date        object
Price       object
Open        object
High        object
Low         object
Vol.        object
Change %    object
dtype: object

# Convertir la columna 'Date' a tipo datetime
df['Date'] = pd.to_datetime(df['Date'], format='%m/%d/%Y')

# Convertir la columna 'Price', 'Open', 'High', 'Low' eliminando comas y convirtiendo a float
df['Price'] = df['Price'].str.replace(',', '').astype(float)
df['Open'] = df['Open'].str.replace(',', '').astype(float)
df['High'] = df['High'].str.replace(',', '').astype(float)
df['Low'] = df['Low'].str.replace(',', '').astype(float)

# Convertir la columna 'Vol.' eliminando comas, reemplazando 'K' por 'e3' (miles) y 'M' por 'e6' (millones), luego convertir a numérico
df['Vol.'] = df['Vol.'].str.replace('K', 'e3').str.replace('M', 'e6').str.replace(',', '')
df['Vol.'] = pd.to_numeric(df['Vol.'], errors='coerce')

# Convertir la columna 'Change %' eliminando el símbolo '%' y convirtiendo a float
df['Change %'] = df['Change %'].str.replace('%', '').astype(float)

# Mostrar los primeros 5 registros después de la conversión
print("Datos después de la conversión a numérico:")
print(df.head())

# Mostrar los tipos de datos después de la conversión
print("\nTipos de datos después de la conversión:")
print(df.dtypes)

Datos después de la conversión a numérico:
        Date    Price     Open     High      Low      Vol.  Change %
0 2024-03-24  67211.9  64036.5  67587.8  63812.9   65590.0      4.96
1 2024-03-23  64037.8  63785.6  65972.4  63074.9   35110.0      0.40
2 2024-03-22  63785.5  65501.5  66633.3  62328.3   72430.0     -2.62
3 2024-03-21  65503.8  67860.0  68161.7  64616.1   75260.0     -3.46
4 2024-03-20  67854.0  62046.8  68029.5  60850.9  133530.0      9.35

Tipos de datos después de la conversión:
Date        datetime64[ns]
Price              float64
Open               float64
High               float64
Low                float64
Vol.               float64
Change %           float64
dtype: object

# Análisis descriptivo con formato estético incluyendo 'dtype'
def descriptive_analysis(df):
    print("Análisis Descriptivo")

    # Resumen estadístico con tipo de dato
    summary = df.describe().T  # Transponemos para mostrar variables como filas

    # Añadir una columna con el tipo de dato (dtype)
    summary['dtype'] = df.dtypes

    print(tabulate(summary, headers="keys", tablefmt="pretty"))

# Ejecutar el análisis descriptivo con presentación mejorada y tipo de datos
descriptive_analysis(df)

Análisis Descriptivo
+----------+--------+---------------------+---------------------+---------------------+---------------------+---------------------+---------------------+--------------------+----------------+
|          | count  |        mean         |         min         |         25%         |         50%         |         75%         |         max         |        std         |     dtype      |
+----------+--------+---------------------+---------------------+---------------------+---------------------+---------------------+---------------------+--------------------+----------------+
|   Date   |  4999  | 2017-05-21 00:00:00 | 2010-07-18 00:00:00 | 2013-12-18 12:00:00 | 2017-05-21 00:00:00 | 2020-10-21 12:00:00 | 2024-03-24 00:00:00 |        nan         | datetime64[ns] |
|  Price   | 4999.0 | 10812.283336667333  |         0.1         |        226.7        |       1975.1        | 15450.150000000001  |       73066.3       | 15892.032468245246 |    float64     |
|   Open   | 4999.0 | 10798.901840368073  |         0.0         |       226.45        |       1962.0        |      15372.15       |       73066.7       | 15872.785452462605 |    float64     |
|   High   | 4999.0 | 11067.453050610124  |         0.1         |        231.4        |       2048.4        |      15954.55       |       73740.9       | 16270.707593648698 |    float64     |
|   Low    | 4999.0 | 10511.891198239648  |         0.0         |       221.95        |       1875.3        |       14557.2       |       71338.4       | 15444.928770647624 |    float64     |
|   Vol.   | 4977.0 |  4520315.993570424  |        80.0         |       31710.0       |       68380.0       |      181810.0       |     752840000.0     | 44956402.24859013  |    float64     |
| Change % | 4999.0 | 0.41575115023004605 |       -57.21        |        -1.17        |         0.0         | 1.7850000000000001  |       336.84        | 7.094771253715175  |    float64     |
+----------+--------+---------------------+---------------------+---------------------+---------------------+---------------------+---------------------+--------------------+----------------+

Identificar si existen datos faltantes

# Verificar si existen datos faltantes en el DataFrame
print("Datos faltantes por columna:")
print(df.isnull().sum())

Datos faltantes por columna:
Date         0
Price        0
Open         0
High         0
Low          0
Vol.        22
Change %     0
dtype: int64

Imputación de datos faltantes

# Aplicar la técnica de imputación (forward fill) para rellenar los valores nulos
df.fillna(method='ffill', inplace=True)

# Verificar si se han rellenado los datos faltantes
print("Datos faltantes por columna después de la imputación:")
print(df.isnull().sum())

Datos faltantes por columna después de la imputación:
Date        0
Price       0
Open        0
High        0
Low         0
Vol.        0
Change %    0
dtype: int64

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_8284\1401077761.py:2: FutureWarning: DataFrame.fillna with 'method' is deprecated and will raise in a future version. Use obj.ffill() or obj.bfill() instead.
  df.fillna(method='ffill', inplace=True)

Gráfico de velas (Candlestick chart)

Gráfico de velas: Visualiza el comportamiento de los precios (apertura, máximo, mínimo, cierre) a lo largo del tiempo.

import plotly.graph_objects as go

# Crear gráfico de velas (candlestick chart)
def plot_candlestick(df):
    fig = go.Figure(data=[go.Candlestick(x=df['Date'],
                                         open=df['Open'],
                                         high=df['High'],
                                         low=df['Low'],
                                         close=df['Price'],
                                         name='Candlestick')])

    # Configuración del título y los ejes
    fig.update_layout(
        title='Gráfico de Velas del Precio de Bitcoin',
        xaxis_title='Fecha',
        yaxis_title='Precio (USD)',
        xaxis_rangeslider_visible=False,  # Ocultar el slider
        template='plotly_white'  # Estilo limpio
    )

    # Mostrar el gráfico
    fig.show()

# Ejecutar el gráfico de velas
plot_candlestick(df)

Vemos una tendencia creciente en el precio del Bitcoin

Histograma del volumen

Histograma del volumen: Muestra la cantidad de volumen tradeado diariamente de forma clara e interactiva.

import plotly.express as px

# Crear el histograma del volumen tradeado diariamente
def plot_volume_histogram(df):
    fig = px.histogram(df, x='Date', y='Vol.', nbins=50, title='Histograma del Volumen Tradeado Diariamente')

    # Configuración del diseño del histograma
    fig.update_layout(
        xaxis_title='Fecha',
        yaxis_title='Volumen Tradeado (USD)',
        template='plotly_white',  # Estilo limpio
        bargap=0.1  # Ajustar el espacio entre barras
    )

    # Mostrar el gráfico
    fig.show()

# Ejecutar el histograma del volumen
plot_volume_histogram(df)

El volumen de tradeo del Bitcoin fue significativamente mas grande en 2022 que el resto de anos, esto puede explicar su precio maximo en esta epoca

Gráficos de Subseries: Gráficos de Series de Tiempo

Para crear gráficos de subseries agrupados por semana, mes y año, utilizando gráficos de series de tiempo y boxplots como se menciona en la imagen, puedes seguir los siguientes pasos:

1. Agrupación de datos por semana, mes y año: Primero, agruparemos los datos por semana, mes y año usando la columna Date para extraer las subseries. Luego, podemos generar gráficos de series temporales y boxplots.

2. Gráficos de series de tiempo: Estos gráficos mostrarán la evolución de los precios (o cualquier otra variable) a lo largo de las subseries (por semana, mes, año).

3. Boxplots: Los boxplots son útiles para comparar la distribución de los precios (o el volumen) dentro de los grupos definidos (semanal, mensual, anual).

Código paso a paso:

Paso 1: Agrupar por semana, mes y año

import pandas as pd

# Asegúrate de que 'Date' sea una columna de tipo datetime
df['Date'] = pd.to_datetime(df['Date'])

# Agregar columnas para semana, mes y año
df['Week'] = df['Date'].dt.isocalendar().week
df['Month'] = df['Date'].dt.month
df['Year'] = df['Date'].dt.year

Paso 2: Gráficos de series temporales por subseries

import plotly.express as px

# Gráfico de series de tiempo por semana
def plot_time_series_week(df):
    fig = px.line(df, x='Date', y='Price', color='Week',
                  title='Precio de Bitcoin por Semana',
                  labels={'Price':'Precio (USD)', 'Date':'Fecha', 'Week':'Semana'})
    fig.show()

# Ejecutar el gráfico de series de tiempo semanal
plot_time_series_week(df)

# Gráfico de series de tiempo por mes
def plot_time_series_month(df):
    fig = px.line(df, x='Date', y='Price', color='Month',
                  title='Precio de Bitcoin por Mes',
                  labels={'Price':'Precio (USD)', 'Date':'Fecha', 'Month':'Mes'})
    fig.show()

# Ejecutar el gráfico de series de tiempo mensual
plot_time_series_month(df)

# Gráfico de series de tiempo por año
def plot_time_series_year(df):
    fig = px.line(df, x='Date', y='Price', color='Year',
                  title='Precio de Bitcoin por Año',
                  labels={'Price':'Precio (USD)', 'Date':'Fecha', 'Year':'Año'})
    fig.show()

# Ejecutar el gráfico de series de tiempo anual
plot_time_series_year(df)

Analizando el grafico de la division anual, semanal y mensual solo podemos afirmar que el precio del bitcoin pese a ser un activo volatil, sigue una tendencia a traves de periodos anuales

Gráficos de Subseries: Boxplots para analizar las subseries

# Boxplot de precios por semana
def plot_boxplot_week(df):
    fig = px.box(df, x='Week', y='Price', title='Distribución del Precio de Bitcoin por Semana',
                 labels={'Price':'Precio (USD)', 'Week':'Semana'})
    fig.show()

# Ejecutar el boxplot semanal
plot_boxplot_week(df)

# Boxplot de precios por mes
def plot_boxplot_month(df):
    fig = px.box(df, x='Month', y='Price', title='Distribución del Precio de Bitcoin por Mes',
                 labels={'Price':'Precio (USD)', 'Month':'Mes'})
    fig.show()

# Ejecutar el boxplot mensual
plot_boxplot_month(df)

# Boxplot de precios por año
def plot_boxplot_year(df):
    fig = px.box(df, x='Year', y='Price', title='Distribución del Precio de Bitcoin por Año',
                 labels={'Price':'Precio (USD)', 'Year':'Año'})
    fig.show()

# Ejecutar el boxplot anual
plot_boxplot_year(df)

Observamos que la distribucion en boxplot por mes, ano y semana nos dice que realmente a traves de los anos el precio del bitcoin ha cambiado bastante. Siendo estos ultimos anos relativamente alto pero en sus primeros anos relativamente bajo

Explicación de cada parte: Agrupación: Las columnas adicionales para semana, mes y año permiten segmentar las series de tiempo en diferentes subseries. Gráficos de series de tiempo: Estos gráficos permiten ver cómo evoluciona el precio de Bitcoin dentro de cada subserie (semana, mes o año). Boxplots: Los boxplots permiten analizar la dispersión y distribución de los precios en las diferentes subseries.

Estudio de Estacionalidad

Para estudiar la estacionariedad de una serie de tiempo utilizando la función de autocorrelación (ACF), el test de Ljung-Box y el test de Dickey-Fuller, podemos seguir los siguientes pasos. También te mostraré cómo aplicar las transformaciones necesarias para convertir la serie en estacionaria si es necesario.

Paso 1: Verificar la estacionariedad con la ACF (Autocorrelation Function) La ACF nos ayuda a observar si existe correlación en los rezagos (lags) de la serie temporal.

Paso 2: Realizar los test estadísticos Test de Ljung-Box: Evalúa si los valores de autocorrelación en todos los rezagos son cercanos a cero, lo que indicaría que no hay correlación y, por lo tanto, la serie es estacionaria. Test de Dickey-Fuller aumentado: Evalúa la hipótesis nula de que una serie tiene una raíz unitaria, lo que implica que no es estacionaria. Paso 3: Transformar la serie de tiempo Si los resultados indican que la serie no es estacionaria, aplicaremos transformaciones como la diferenciación para convertir la serie en estacionaria.

Código paso a paso Importar las librerías necesarias:

import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.graphics.tsaplots import plot_acf
from statsmodels.tsa.stattools import adfuller, acf, q_stat
from statsmodels.stats.diagnostic import acorr_ljungbox

8.1 Gráfico de ACF para verificar autocorrelación

# Gráfico de autocorrelación (ACF) para la columna 'Price'
def plot_acf_chart(df):
    plt.figure(figsize=(10, 6))
    plot_acf(df['Price'], lags=40)  # Mostrar los primeros 40 rezagos
    plt.title('Función de Autocorrelación (ACF) del Precio de Bitcoin')
    plt.show()

# Ejecutar el gráfico de ACF
plot_acf_chart(df)

<Figure size 1000x600 with 0 Axes>

En el gráfico que has generado, la Función de Autocorrelación (ACF) muestra una alta autocorrelación significativa en todos los rezagos (lags), lo cual es un indicador de que la serie no es estacionaria. En una serie estacionaria, las autocorrelaciones deberían disminuir rápidamente a medida que aumenta el número de rezagos, mientras que aquí todas las barras están cerca de 1, lo que indica una fuerte correlación a lo largo del tiempo.

Próximos pasos: Test de Dickey-Fuller: Este test confirmará si la serie tiene una raíz unitaria (no estacionaria). Transformación de la serie: Si la serie no es estacionaria, podemos aplicar la diferenciación para convertirla en estacionaria.

8.2 Test de Ljung-Box

# Test de Ljung-Box para verificar si la serie es autocorrelacionada
def ljung_box_test(df):
    lb_test = acorr_ljungbox(df['Price'], lags=[10], return_df=True)
    print("Resultados del Test de Ljung-Box:")
    print(lb_test)

# Ejecutar el test de Ljung-Box
ljung_box_test(df)

Resultados del Test de Ljung-Box:
         lb_stat  lb_pvalue
10  48871.328172        0.0

Interpretación: Un valor p de 0.0 indica que rechazamos la hipótesis nula de que no hay autocorrelación en los rezagos. Esto significa que hay autocorrelación significativa en la serie temporal, lo que sugiere que no es estacionaria.

Interpretación: Un valor p de 0.0 indica que rechazamos la hipótesis nula de que no hay autocorrelación en los rezagos. Esto significa que hay autocorrelación significativa en la serie temporal, lo que sugiere que no es estacionaria.

# Test de Dickey-Fuller aumentado
def adfuller_test(df):
    result = adfuller(df['Price'])
    print('Resultados del Test de Dickey-Fuller:')
    print(f'Estadístico ADF: {result[0]}')
    print(f'Valor P: {result[1]}')
    print(f'Valores Críticos:')
    for key, value in result[4].items():
        print(f'   {key}: {value}')

# Ejecutar el test de Dickey-Fuller
adfuller_test(df)

Resultados del Test de Dickey-Fuller:
Estadístico ADF: -2.685797950257254
Valor P: 0.07652825121387355
Valores Críticos:
   1%: -3.4316674956516784
   5%: -2.8621221897344484
   10%: -2.567079900452355

Interpretación: El valor p es 0.0756, que es mayor a 0.05, lo que significa que no podemos rechazar la hipótesis nula de que la serie tiene una raíz unitaria. Esto implica que la serie no es estacionaria.

Además, el estadístico ADF (-2.68) no es más pequeño que los valores críticos a los niveles del 1%, 5%, o incluso el 10%, lo que refuerza la conclusión de que la serie no es estacionaria.

Transformar la serie para hacerla estacionaria

from statsmodels.tsa.seasonal import seasonal_decompose
import matplotlib.pyplot as plt

# Asegurarse de que los datos están ordenados por fecha
df = df.sort_values(by='Date')

# Descomponer la serie en tendencia, estacionalidad y residuo
decomposed = seasonal_decompose(df['Price'], model='multiplicative', period=30)  # Ajustar 'period' según el ciclo

# Graficar los componentes
decomposed.plot()
plt.show()

from statsmodels.graphics.tsaplots import plot_acf
from statsmodels.tsa.stattools import adfuller

# Graficar la ACF de los residuos
plot_acf(decomposed.resid.dropna(), lags=40)
plt.title('ACF de los Residuos')
plt.show()

# Aplicar el Test de Dickey-Fuller en los residuos
result_adf = adfuller(decomposed.resid.dropna())
print(f'Estadístico ADF: {result_adf[0]}')
print(f'Valor P: {result_adf[1]}')
print(f'Valores Críticos: {result_adf[4]}')

Estadístico ADF: -15.674313207396887
Valor P: 1.499403070029146e-28
Valores Críticos: {'1%': np.float64(-3.4316752386670926), '5%': np.float64(-2.86212561054255), '10%': np.float64(-2.5670817214845068)}

Agregación por grupos (semanas, días, meses) y Cálculo de estadísticas móviles**

Agregacion por grupos:

# Asegúrate de que la columna 'Date' esté en formato datetime
df['Date'] = pd.to_datetime(df['Date'])

# Agregar por semana
weekly_data = df.resample('W', on='Date').agg({'Price': ['mean', 'std']})

# Agregar por mes
monthly_data = df.resample('M', on='Date').agg({'Price': ['mean', 'std']})

# Agregar por día
daily_data = df.resample('D', on='Date').agg({'Price': ['mean', 'std']})

# Mostrar el resultado
print("Datos semanales (media y desviación estándar):")
print(weekly_data.head())

print("\nDatos mensuales (media y desviación estándar):")
print(monthly_data.head())

print("\nDatos diarios (media y desviación estándar):")
print(daily_data.head())

Datos semanales (media y desviación estándar):
           Price     
            mean  std
Date                 
2010-07-18   0.1  NaN
2010-07-25   0.1  0.0
2010-08-01   0.1  0.0
2010-08-08   0.1  0.0
2010-08-15   0.1  0.0

Datos mensuales (media y desviación estándar):
               Price          
                mean       std
Date                          
2010-07-31  0.100000  0.000000
2010-08-31  0.100000  0.000000
2010-09-30  0.100000  0.000000
2010-10-31  0.119355  0.040161
2010-11-30  0.263333  0.055605

Datos diarios (media y desviación estándar):
           Price    
            mean std
Date                
2010-07-18   0.1 NaN
2010-07-19   0.1 NaN
2010-07-20   0.1 NaN
2010-07-21   0.1 NaN
2010-07-22   0.1 NaN

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_8284\1942824804.py:8: FutureWarning:

'M' is deprecated and will be removed in a future version, please use 'ME' instead.

Comportamiento de la media y desviación estándar

# Convertir la columna 'Date' a tipo datetime
df['Date'] = pd.to_datetime(df['Date'], format='%Y-%m-%d')

# Agrupar los datos por semana, mes y año y calcular la media y la desviación estándar
weekly_data = df.resample('W', on='Date').agg({'Price': ['mean', 'std']})
monthly_data = df.resample('M', on='Date').agg({'Price': ['mean', 'std']})
annual_data = df.resample('Y', on='Date').agg({'Price': ['mean', 'std']})

# Graficar el comportamiento de la media y desviación estándar por semanas
plt.figure(figsize=(10, 6))
plt.plot(weekly_data.index, weekly_data['Price']['mean'], label='Media Semanal', color='blue')
plt.fill_between(weekly_data.index, weekly_data['Price']['mean'] - weekly_data['Price']['std'],
                 weekly_data['Price']['mean'] + weekly_data['Price']['std'], color='blue', alpha=0.2)
plt.title('Comportamiento de la Media y Desviación Estándar Semanal')
plt.xlabel('Fecha')
plt.ylabel('Precio')
plt.legend()
plt.xticks(rotation=45)
plt.show()

# Graficar para los datos mensuales
plt.figure(figsize=(10, 6))
plt.plot(monthly_data.index, monthly_data['Price']['mean'], label='Media Mensual', color='green')
plt.fill_between(monthly_data.index, monthly_data['Price']['mean'] - monthly_data['Price']['std'],
                 monthly_data['Price']['mean'] + monthly_data['Price']['std'], color='green', alpha=0.2)
plt.title('Comportamiento de la Media y Desviación Estándar Mensual')
plt.xlabel('Fecha')
plt.ylabel('Precio')
plt.legend()
plt.xticks(rotation=45)
plt.show()

# Graficar el comportamiento de la media y desviación estándar anual
plt.figure(figsize=(10, 6))
plt.plot(annual_data.index, annual_data['Price']['mean'], label='Media Anual', color='purple')
plt.fill_between(annual_data.index, annual_data['Price']['mean'] - annual_data['Price']['std'],
                 annual_data['Price']['mean'] + annual_data['Price']['std'], color='purple', alpha=0.2)
plt.title('Comportamiento de la Media y Desviación Estándar Anual')
plt.xlabel('Fecha')
plt.ylabel('Precio')
plt.legend()
plt.xticks(rotation=45)
plt.show()

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_8284\3000577512.py:6: FutureWarning:

'M' is deprecated and will be removed in a future version, please use 'ME' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_8284\3000577512.py:7: FutureWarning:

'Y' is deprecated and will be removed in a future version, please use 'YE' instead.

En estas graficas vemos como pese a que la desviacion standard diaria no es alta, la anual gracias a la gran robustez de datos si es mayor

Estadisticos Moviles

# Media y desviación estándar móviles con ventana de 30 días
df['Mean_Mobile'] = df['Price'].rolling(window=30).mean()
df['Std_Mobile'] = df['Price'].rolling(window=30).std()

# Graficar la media móvil y la desviación estándar móvil
plt.figure(figsize=(10, 6))
plt.plot(df['Date'], df['Mean_Mobile'], label='Media Móvil (30 días)', color='blue')
plt.fill_between(df['Date'], df['Mean_Mobile'] - df['Std_Mobile'],
                 df['Mean_Mobile'] + df['Std_Mobile'], color='blue', alpha=0.2)
plt.title('Media Móvil y Desviación Estándar Móvil (30 días)')
plt.xlabel('Fecha')
plt.ylabel('Precio')
plt.legend()
plt.xticks(rotation=45)
plt.show()

Distribucion de frecuencia para diferentes lags

import seaborn as sns
import matplotlib.pyplot as plt

# Diferencias con diferentes lags
df['Price_diff_1'] = df['Price'].diff(1)  # Lag de 1 día
df['Price_diff_7'] = df['Price'].diff(7)  # Lag de 1 semana
df['Price_diff_30'] = df['Price'].diff(30)  # Lag de 1 mes

# Graficar la distribución de las diferencias para diferentes lags
plt.figure(figsize=(10, 6))
sns.histplot(df['Price_diff_1'].dropna(), label='Lag 1 día', color='blue', kde=True)
sns.histplot(df['Price_diff_7'].dropna(), label='Lag 7 días', color='green', kde=True)
sns.histplot(df['Price_diff_30'].dropna(), label='Lag 30 días', color='red', kde=True)
plt.title('Distribución de Frecuencias para Diferentes Lags')
plt.xlabel('Diferencias de Precio')
plt.ylabel('Frecuencia')
plt.ylim(0, 1100)  # Ajustar el eje Y a un máximo de 1100
plt.legend()
plt.show()

Aplicación de las medias móviles

• Medias móviles: Se calculan medias móviles para diferentes ventanas (2, 3, 4 días) y se comparan con la serie original.

• Remover tendencia: La serie se suaviza con una media móvil y se elimina la tendencia restando la media móvil de la serie original.

• Pruebas de estacionariedad: Aplicamos el test de Dickey-Fuller y el test de Ljung-Box para verificar si la serie sin tendencia es estacionaria.

Aplicamos las medias moviles

# Medias móviles de diferentes órdenes
df['M2'] = df['Price'].rolling(window=2).mean()
df['M4'] = df['Price'].rolling(window=4).mean()
df['M3'] = df['Price'].rolling(window=3).mean()

# Visualizar las medias móviles junto con la serie original
plt.figure(figsize=(10, 6))
plt.plot(df['Date'], df['Price'], label='Precio Original', color='black')
plt.plot(df['Date'], df['M2'], label='Media Móvil (2 días)', color='blue')
plt.plot(df['Date'], df['M4'], label='Media Móvil (4 días)', color='green')
plt.plot(df['Date'], df['M3'], label='Media Móvil (3 días)', color='red')
plt.title('Medias Móviles de Diferentes Ventanas')
plt.xlabel('Fecha')
plt.ylabel('Precio')
plt.legend()
plt.xticks(rotation=45)
plt.show()

Removemos la tendencia con la media movil

# Remover la tendencia restando la media móvil de 4 días de la serie original
df['Detrended'] = df['Price'] - df['M4']

# Graficar la serie sin tendencia
plt.figure(figsize=(10, 6))
plt.plot(df['Date'], df['Detrended'], label='Serie sin Tendencia', color='purple')
plt.title('Serie de Precios sin Tendencia (Media Móvil 4 días)')
plt.xlabel('Fecha')
plt.ylabel('Precio Detrended')
plt.legend()
plt.xticks(rotation=45)
plt.show()

Pruebas de estacionariedad (Dickey-Fuller y Ljung-Box):

from statsmodels.tsa.stattools import adfuller
from statsmodels.stats.diagnostic import acorr_ljungbox

# Aplicar la prueba de Dickey-Fuller en la serie sin tendencia
adf_result = adfuller(df['Detrended'].dropna())
print(f'Estadístico ADF: {adf_result[0]}')
print(f'Valor P: {adf_result[1]}')

# Aplicar la prueba de Ljung-Box en la serie sin tendencia
ljungbox_result = acorr_ljungbox(df['Detrended'].dropna(), lags=[10], return_df=True)
print(ljungbox_result)

Estadístico ADF: -9.249080004579481
Valor P: 1.5093100712032719e-15
        lb_stat  lb_pvalue
10  1894.301002        0.0

Prueba de Dickey-Fuller (ADF):

Interpretación: Dado que el valor p es mucho menor a 0.05, puedes rechazar la hipótesis nula de que la serie tiene una raíz unitaria, lo que significa que la serie sin tendencia es estacionaria.

Prueba de Ljung-Box:

Interpretación: Un valor p de 0.0 en la prueba de Ljung-Box sugiere que hay autocorrelación significativa en los residuos. Esto significa que, aunque la serie sea estacionaria según la prueba de Dickey-Fuller, aún hay dependencia temporal (autocorrelación) que debe ser explicada o modelada.

Descomposición de la serie temporal del precio de cierre de BTC-USD

Descomposicion con medias moviles

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import seasonal_decompose

# Aplicar media móvil de 7 días para suavizar
df['Price_MA7'] = df['Price'].rolling(window=7).mean()

# Graficar la serie original y la suavizada
plt.figure(figsize=(10, 6))
plt.plot(df['Date'], df['Price'], label='Precio Original', color='black')
plt.plot(df['Date'], df['Price_MA7'], label='Media Móvil 7 días', color='blue')
plt.title('Precio Original vs. Media Móvil (7 días)')
plt.xlabel('Fecha')
plt.ylabel('Precio')
plt.legend()
plt.xticks(rotation=45)
plt.show()

# Descomposición de la serie temporal usando statsmodels.tsa
decomposed = seasonal_decompose(df['Price_MA7'].dropna(), model='additive', period=30)

# Graficar la descomposición
decomposed.plot()
plt.show()

Verificación de la independencia de los residuos (Prueba de Ljung-Box)

from statsmodels.stats.diagnostic import acorr_ljungbox

# Obtener los residuos de la descomposición
residuos = decomposed.resid.dropna()

# Aplicar la prueba de Ljung-Box en los residuos
ljungbox_result = acorr_ljungbox(residuos, lags=[10], return_df=True)

# Mostrar los resultados de la prueba
print(ljungbox_result)

        lb_stat  lb_pvalue
10  14625.69533        0.0

El valor p extremadamente pequeño sugiere que existe autocorrelación significativa en los residuos. Esto implica que la descomposición realizada aún no ha eliminado toda la dependencia temporal en los residuos.

Analisis de la serie de BITCOIN para el retorno acumulado diario AT y las volatilidades

import pandas as pd


df = pd.read_csv(BHdata)
# Convertir la columna 'Date' a tipo datetime
df['Date'] = pd.to_datetime(df['Date'], format='%m/%d/%Y')

# Convertir las columnas 'Price', 'Open', 'High', 'Low' eliminando comas y convirtiendo a float
df['Price'] = pd.to_numeric(df['Price'].str.replace(',', ''), errors='coerce')
df['Open'] = pd.to_numeric(df['Open'].str.replace(',', ''), errors='coerce')
df['High'] = pd.to_numeric(df['High'].str.replace(',', ''), errors='coerce')
df['Low'] = pd.to_numeric(df['Low'].str.replace(',', ''), errors='coerce')

# Convertir la columna 'Vol.' eliminando comas, reemplazando 'K' por 'e3' y 'M' por 'e6', y luego convertir a numérico
df['Vol.'] = df['Vol.'].str.replace('K', 'e3').str.replace('M', 'e6').str.replace(',', '')
df['Vol.'] = pd.to_numeric(df['Vol.'], errors='coerce')

# Convertir la columna 'Change %' eliminando el símbolo '%' y convirtiendo a float
df['Change %'] = df['Change %'].str.replace('%', '').astype(float)

# Eliminar las filas con valores nulos en la columna 'Price'
df.dropna(subset=['Price'], inplace=True)

# Calcular el retorno diario Rt
df['Rt'] = (df['Price'] - df['Price'].shift(1)) / df['Price'].shift(1)

# Calcular el retorno acumulado diario At
df['At'] = df['Rt'].cumsum()

# Función para calcular la volatilidad usando ventanas móviles
def calcular_volatilidad(data, ventana):
    """
    Esta función calcula la volatilidad (desviación estándar) 
    de los retornos diarios utilizando una ventana móvil.
    """
    return data['Rt'].rolling(window=ventana).std()

# Calcular volatilidad para diferentes ventanas
ventanas = [7, 14, 21, 28]
for ventana in ventanas:
    df[f'Volatilidad_{ventana}'] = calcular_volatilidad(df, ventana)

# Mostrar los primeros 10 registros con las nuevas columnas de volatilidad
print(df[['Date', 'At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']].head(15))

         Date        At  Volatilidad_7  Volatilidad_14  Volatilidad_21  \
0  2024-03-24       NaN            NaN             NaN             NaN   
1  2024-03-23 -0.047225            NaN             NaN             NaN   
2  2024-03-22 -0.051165            NaN             NaN             NaN   
3  2024-03-21 -0.024226            NaN             NaN             NaN   
4  2024-03-20  0.011652            NaN             NaN             NaN   
5  2024-03-19 -0.073884            NaN             NaN             NaN   
6  2024-03-18  0.015465            NaN             NaN             NaN   
7  2024-03-17  0.027257       0.057142             NaN             NaN   
8  2024-03-16 -0.017734       0.056814             NaN             NaN   
9  2024-03-15  0.045797       0.060785             NaN             NaN   
10 2024-03-14  0.073492       0.060813             NaN             NaN   
11 2024-03-13  0.097009       0.060247             NaN             NaN   
12 2024-03-12  0.075165       0.046199             NaN             NaN   
13 2024-03-11  0.083964       0.035128             NaN             NaN   
14 2024-03-10  0.040492       0.040414         0.04756             NaN   

    Volatilidad_28  
0              NaN  
1              NaN  
2              NaN  
3              NaN  
4              NaN  
5              NaN  
6              NaN  
7              NaN  
8              NaN  
9              NaN  
10             NaN  
11             NaN  
12             NaN  
13             NaN  
14             NaN  

# Análisis descriptivo con formato estético incluyendo 'dtype'
def descriptive_analysis(df):
    print("Análisis Descriptivo")

    # Resumen estadístico con tipo de dato
    summary = df.describe().T  # Transponemos para mostrar variables como filas

    # Añadir una columna con el tipo de dato (dtype)
    summary['dtype'] = df.dtypes

    print(tabulate(summary, headers="keys", tablefmt="pretty"))

# Ejecutar el análisis descriptivo con presentación mejorada y tipo de datos
descriptive_analysis(df)

Análisis Descriptivo
+----------------+--------+------------------------+---------------------+-----------------------+----------------------+----------------------+---------------------+----------------------+----------------+
|                | count  |          mean          |         min         |          25%          |         50%          |         75%          |         max         |         std          |     dtype      |
+----------------+--------+------------------------+---------------------+-----------------------+----------------------+----------------------+---------------------+----------------------+----------------+
|      Date      |  4999  |  2017-05-21 00:00:00   | 2010-07-18 00:00:00 |  2013-12-18 12:00:00  | 2017-05-21 00:00:00  | 2020-10-21 12:00:00  | 2024-03-24 00:00:00 |         nan          | datetime64[ns] |
|     Price      | 4999.0 |   10812.283336667333   |         0.1         |         226.7         |        1975.1        |  15450.150000000001  |       73066.3       |  15892.032468245246  |    float64     |
|      Open      | 4999.0 |   10798.901840368073   |         0.0         |        226.45         |        1962.0        |       15372.15       |       73066.7       |  15872.785452462605  |    float64     |
|      High      | 4999.0 |   11067.453050610124   |         0.1         |         231.4         |        2048.4        |       15954.55       |       73740.9       |  16270.707593648698  |    float64     |
|      Low       | 4999.0 |   10511.891198239648   |         0.0         |        221.95         |        1875.3        |       14557.2        |       71338.4       |  15444.928770647624  |    float64     |
|      Vol.      | 4977.0 |   4520315.993570424    |        80.0         |        31710.0        |       68380.0        |       181810.0       |     752840000.0     |  44956402.24859013   |    float64     |
|    Change %    | 4999.0 |  0.41575115023004605   |       -57.21        |         -1.17         |         0.0          |  1.7850000000000001  |       336.84        |  7.094771253715175   |    float64     |
|       Rt       | 4998.0 | -0.0008649416107884587 | -0.7710335525206542 | -0.018043005662710842 |         0.0          | 0.012381674779143557 | 1.3369079535299373  | 0.060963078744488954 |    float64     |
|       At       | 4998.0 |  -1.7488420320226186   | -5.0729781707207176 |  -2.8795951025620825  |  -1.339525597017683  | -0.7968745330235159  | 0.7233894556997841  |  1.308646419197632   |    float64     |
| Volatilidad_7  | 4992.0 |  0.04004272329136203   |         0.0         | 0.017841963196907742  | 0.028731243369467502 | 0.045641369317982274 | 0.7425252346415011  | 0.046675532410058646 |    float64     |
| Volatilidad_14 | 4985.0 |  0.04254656625278011   |         0.0         | 0.020570255012699223  | 0.031840592334259225 | 0.04809342031022853  | 0.5133244328337819  | 0.04381810312793947  |    float64     |
| Volatilidad_21 | 4978.0 |  0.04386830333712439   |         0.0         | 0.022328891704747465  |  0.0329581872933121  | 0.048341492502098536 | 0.4172879234974023  | 0.04233204152371323  |    float64     |
| Volatilidad_28 | 4971.0 |  0.044800297271042205  |         0.0         | 0.023726993331419644  | 0.03345168952269009  | 0.049422096425338735 | 0.36087652079242866 | 0.041310540523075305 |    float64     |
+----------------+--------+------------------------+---------------------+-----------------------+----------------------+----------------------+---------------------+----------------------+----------------+

Revision de datos faltantes y imputacion de estos

# Verificar si existen datos faltantes en el DataFrame
print("Datos faltantes por columna:")
print(df.isnull().sum())

# Aplicar la técnica de imputación (forward fill) para rellenar los valores nulos
df.fillna(method='ffill', inplace=True)

# Verificar si se han rellenado los datos faltantes
print("Datos faltantes por columna después de la imputación:")
print(df.isnull().sum())
# Calcular los retornos y volatilidades (suponiendo que ya lo has hecho)

# Eliminar las filas con valores nulos en las columnas 'Rt', 'At' y las volatilidades
df.dropna(subset=['Rt', 'At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28'], inplace=True)

# Verificar si aún existen datos faltantes
print("Datos faltantes por columna después de eliminar filas con NaN:")
print(df.isnull().sum())

Datos faltantes por columna:
Date               0
Price              0
Open               0
High               0
Low                0
Vol.              22
Change %           0
Rt                 1
At                 1
Volatilidad_7      7
Volatilidad_14    14
Volatilidad_21    21
Volatilidad_28    28
dtype: int64

Datos faltantes por columna después de la imputación:
Date               0
Price              0
Open               0
High               0
Low                0
Vol.               0
Change %           0
Rt                 1
At                 1
Volatilidad_7      7
Volatilidad_14    14
Volatilidad_21    21
Volatilidad_28    28
dtype: int64
Datos faltantes por columna después de eliminar filas con NaN:
Date              0
Price             0
Open              0
High              0
Low               0
Vol.              0
Change %          0
Rt                0
At                0
Volatilidad_7     0
Volatilidad_14    0
Volatilidad_21    0
Volatilidad_28    0
dtype: int64

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_8284\3424944515.py:6: FutureWarning:

DataFrame.fillna with 'method' is deprecated and will raise in a future version. Use obj.ffill() or obj.bfill() instead.

Graficos de Velas para At

import plotly.graph_objects as go

# Crear gráfico de velas (candlestick chart)
def plot_candlestick(df):
    fig = go.Figure(data=[go.Candlestick(x=df['Date'],
                                         open=df['Open'],
                                         high=df['High'],
                                         low=df['Low'],
                                         close=df['At'],
                                         name='Candlestick')])

    # Configuración del título y los ejes
    fig.update_layout(
        title='Gráfico de Velas del retorno acumulado del Bitcoin',
        xaxis_title='Fecha',
        yaxis_title='Retorno acumulado diario (USD)',
        xaxis_rangeslider_visible=False,  # Ocultar el slider
        template='plotly_white'  # Estilo limpio
    )

    # Mostrar el gráfico
    fig.show()

# Ejecutar el gráfico de velas
plot_candlestick(df)

Analisis del grafico de velas del AT del Bitcoin

El gráfico de velas de los retornos acumulados de Bitcoin en estos últimos 14 años me muestra cómo ha tenido picos de crecimiento impresionantes, con subidas fuertes en momentos como 2017 y luego entre 2020 y 2021. Entre esos picos veo también caídas marcadas, como en 2018 y otra en 2022, que destacan la volatilidad de este mercado. A pesar de esas correcciones, lo que se ve es una tendencia a que, cada vez que retrocede, termina alcanzando nuevos máximos en el largo plazo.

Histograma de las Volatilidades

import plotly.express as px

# Crear el histograma de las volatilidades
def plot_volatility_histogram(df, volatility_column):
    fig = px.histogram(df, x=volatility_column, nbins=50, title=f'Histograma de {volatility_column}')

    # Configuración del diseño del histograma
    fig.update_layout(
        xaxis_title='Volatilidad',
        yaxis_title='Frecuencia',
        template='plotly_white',  # Estilo limpio
        bargap=0.1  # Ajustar el espacio entre barras
    )

    # Mostrar el gráfico
    fig.show()

# Ejecutar el histograma para 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21' y 'Volatilidad_28'
volatility_columns = ['Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']
for col in volatility_columns:
    plot_volatility_histogram(df, col)

Analisis del histograma de las volatilidades

Al ver estos histogramas de volatilidad de Bitcoin con ventanas de 7, 14, 21 y 28 días, noto que todos muestran una distribución similar. La mayor parte de la volatilidad se concentra en niveles bajos, especialmente entre 0 y 0.05, sin importar la longitud de la ventana. Esto me indica que, independientemente del período de observación, la volatilidad de Bitcoin tiende a mantenerse en valores reducidos la mayoría del tiempo.

Sin embargo, en todos los histogramas hay algunas observaciones en rangos más altos, alrededor de 0.05 a 0.15, que son menos frecuentes pero marcan episodios de volatilidad alta que ocurren esporádicamente. Más allá de 0.15, los valores son todavía menos comunes, lo cual es consistente en todas las ventanas. Esto sugiere que los picos de volatilidad, aunque presentes, no son la norma y se presentan como eventos aislados, manteniendo una estructura estable en los datos de volatilidad acumulada en diferentes periodos.

Graficos de subseries de tiempo para las volatilidades y para At

import pandas as pd
import plotly.express as px

# Asegúrate de que 'Date' sea una columna de tipo datetime
df['Date'] = pd.to_datetime(df['Date'], format='%m/%d/%Y')

# Agregar columnas para semana, mes y año
df['Week'] = df['Date'].dt.isocalendar().week
df['Month'] = df['Date'].dt.month
df['Year'] = df['Date'].dt.year

# Función para graficar la serie de tiempo
def graficar_serie_tiempo(df, columna, freq, titulo):
    # Agrupar por frecuencia y calcular el promedio
    if freq == 'semanal':
        df_grouped = df.groupby(['Year', 'Week']).mean().reset_index()
        x = df_grouped['Year'].astype(str) + '-W' + df_grouped['Week'].astype(str)
    elif freq == 'mensual':
        df_grouped = df.groupby(['Year', 'Month']).mean().reset_index()
        x = df_grouped['Year'].astype(str) + '-M' + df_grouped['Month'].astype(str)
    elif freq == 'anual':
        df_grouped = df.groupby('Year').mean().reset_index()
        x = df_grouped['Year'].astype(str)
    
    # Graficar
    fig = px.line(df_grouped, x=x, y=columna, title=titulo)
    fig.update_layout(xaxis_title='Fecha', yaxis_title=columna, template='plotly_white')
    fig.show()

# Graficar cada una de las volatilidades y At en frecuencias semanales, mensuales y anuales
volatilidades = ['Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28', 'At']
frecuencias = ['semanal', 'mensual', 'anual']

for volatilidad in volatilidades:
    for freq in frecuencias:
        graficar_serie_tiempo(df, volatilidad, freq, f'{volatilidad} ({freq.capitalize()})')

Analisis de la descomposicion por tiempo de la volatilidad

Al observar estos 12 gráficos de la serie de tiempo de la volatilidad del Bitcoin, divididos en ventanas semanal, mensual y anual, noto un patrón interesante. Conforme aumenta la ventana con la que se mide la volatilidad, esta muestra más variación y picos, especialmente en las ventanas semanales. Esto significa que en periodos cortos, la volatilidad tiende a moverse de manera más abrupta y refleja mejor los eventos inmediatos que afectan el mercado.

Sin embargo, cuando analizo la volatilidad en periodos mayores, como las ventanas mensuales y, especialmente, en las anuales, noto que la variación disminuye considerablemente. La volatilidad se suaviza y fluctúa menos, mostrando un comportamiento más estable en el largo plazo. Esto me indica que, aunque Bitcoin es un activo volátil a corto plazo, en el horizonte anual su volatilidad presenta una tendencia a estabilizarse. Este análisis resalta cómo, dependiendo de la ventana y el período de observación, puedo obtener una percepción distinta sobre la estabilidad del mercado de Bitcoin: alta variabilidad a corto plazo, pero relativa estabilidad cuando se ve en un contexto de largo plazo.

Analisis de la descomposicion por tiempo de At

Al analizar estos cuatro gráficos de los retornos acumulados del Bitcoin, noto un patrón similar al de la volatilidad en cuanto a cómo varía según la ventana de medición. A medida que aumento la ventana para calcular los retornos acumulados, veo mayores fluctuaciones en el corto plazo, reflejando de manera más clara las subidas y caídas abruptas del mercado en periodos de tiempo más pequeños.

Sin embargo, al observar los retornos acumulados en ventanas más largas, las fluctuaciones comienzan a suavizarse, mostrando una trayectoria más estable y creciente. Esto me indica que, aunque el Bitcoin es altamente volátil en el corto plazo, en un horizonte más amplio, los retornos acumulados reflejan una tendencia más positiva y consistente. Esta comparación me permite ver que, a corto plazo, los retornos están mucho más influenciados por la volatilidad, mientras que en el largo plazo la perspectiva de crecimiento se vuelve más clara y menos afectada por las variaciones diarias o semanales.

Subseries pero con Boxplot

import plotly.express as px

# Función ajustada para graficar box plots con cajas visibles
def graficar_boxplot(df, columna, freq, titulo):
    # Agrupar por frecuencia
    if freq == 'semanal':
        df['Semana_Año'] = df['Date'].dt.strftime('%Y-W%U')
        x = 'Semana_Año'
    elif freq == 'mensual':
        df['Mes_Año'] = df['Date'].dt.strftime('%Y-%m')
        x = 'Mes_Año'
    elif freq == 'anual':
        x = 'Year'

    # Graficar box plot, eliminando puntos adicionales para mostrar las cajas claramente
    fig = px.box(df, x=x, y=columna, title=titulo)
    fig.update_layout(
        xaxis_title='Fecha',
        yaxis_title=columna,
        template='plotly_white'
    )
    fig.show()

# Graficar box plots para cada volatilidad y At en frecuencias semanales, mensuales y anuales
volatilidades = ['Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28', 'At']
frecuencias = ['semanal', 'mensual', 'anual']

for volatilidad in volatilidades:
    for freq in frecuencias:
        graficar_boxplot(df, volatilidad, freq, f'Box Plot de {volatilidad} ({freq.capitalize()})')

Analisis graficos Boxplot para la volatilidad

Al observar estos 12 gráficos boxplot de la serie de tiempo de la volatilidad del Bitcoin, divididos en ventanas semanal, mensual y anual, noto un patrón claro en cómo la volatilidad se comporta en diferentes horizontes temporales. En los boxplots semanales, la variación es tan alta que las cajas no logran formarse bien, y lo que predomina son muchos puntos dispersos. Esto me indica que, a corto plazo, la volatilidad es extremadamente variable, con cambios bruscos y constantes que reflejan los movimientos erráticos del mercado de Bitcoin.

Cuando paso a los boxplots de ventanas mensuales, noto que aunque aún hay puntos dispersos, empieza a formarse una estructura más clara en las cajas, con una menor dispersión que en las semanas. Esto sugiere que, aunque persisten los cambios, la volatilidad empieza a estabilizarse un poco cuando se considera en un horizonte intermedio.

Finalmente, al observar los gráficos de ventanas anuales, veo cajas mucho más definidas y una dispersión notablemente menor. Aquí la variabilidad de la volatilidad se reduce considerablemente, mostrando que a mayor plazo la volatilidad se comporta de forma más estable. Este análisis me confirma que, mientras que a corto plazo el Bitcoin es altamente volátil, en periodos largos esta volatilidad se modera, lo cual es útil para tener una visión más equilibrada de su comportamiento en el largo plazo.

Analisis Boxplot para los retornos acumulados (AT)

Al ver estos cuatro gráficos boxplot de los retornos acumulados del Bitcoin, noto un patrón similar al de la volatilidad en términos de cómo la variación cambia con la ventana de medición. En los gráficos con ventanas más cortas, los retornos acumulados muestran una alta dispersión, con muchos puntos individuales fuera de las cajas, lo cual indica una variabilidad considerable y refleja los cambios bruscos que caracterizan al Bitcoin en periodos más cortos.

A medida que se amplía la ventana, veo que los boxplots empiezan a tener cajas más definidas y menos puntos dispersos. Esto sugiere que los retornos acumulados comienzan a estabilizarse cuando se miran en horizontes más largos. En las ventanas más amplias, los boxplots muestran una estructura más compacta y una variación menor en los retornos acumulados, lo que indica que, aunque el Bitcoin puede ser muy volátil en el corto plazo, sus retornos acumulados tienden a estabilizarse en el largo plazo. Esto me da una perspectiva de que, aunque el mercado puede ser inestable a corto plazo, el crecimiento acumulado de Bitcoin muestra una trayectoria más constante y menos influida por las variaciones diarias.

Ahora haremos los graficos ACF para At y cada uno de las volatilidades

import matplotlib.pyplot as plt
from statsmodels.graphics.tsaplots import plot_acf

# Función para graficar ACF
def graficar_acf(serie, titulo):
    plt.figure(figsize=(10, 6))
    plot_acf(serie.dropna(), lags=40)  # Se eliminan valores nulos y se usa un lag de hasta 40 períodos
    plt.title(f'ACF de {titulo}')
    plt.show()

# Graficar ACF para cada volatilidad y At
series = ['Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28', 'At']

for serie in series:
    graficar_acf(df[serie], serie)

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Analisis bandas ACF para la volatilidad y retornos acumulados

Al analizar estos cuatro gráficos de la función de autocorrelación (ACF) de la serie de tiempo de la volatilidad del Bitcoin, noto que todos muestran una espina descendente con los rezagos claramente por fuera de la banda de significancia. Esto me indica una fuerte correlación entre los valores de la volatilidad a lo largo del tiempo, lo cual sugiere que la volatilidad del Bitcoin es altamente persistente: los valores actuales están fuertemente influenciados por los valores pasados. Esta “espina” que va decayendo gradualmente es típica de una serie donde los cambios en la volatilidad tienden a prolongarse antes de disminuir, mostrando una memoria larga en la serie.

Por otro lado, el gráfico de ACF del retorno acumulado es aún más extremo, con todos los rezagos alineados de manera recta y significativamente por encima de la banda de significancia, alcanzando el límite superior. Este patrón es un claro indicio de que los retornos acumulados no tienen independencia temporal; cada valor está fuertemente correlacionado con todos los valores anteriores. Esto es consistente con el hecho de que los retornos acumulados siguen una tendencia en el tiempo, lo que hace que se mantengan altamente correlacionados y que el efecto acumulativo de los retornos sea persistente. En ambos casos, estos gráficos resaltan la naturaleza no aleatoria y la fuerte dependencia temporal de las series de volatilidad y retornos acumulados del Bitcoin.

Pruebas Ljunj box y Dickey Fuller para At y las volatilidades

from statsmodels.tsa.stattools import adfuller
from statsmodels.stats.diagnostic import acorr_ljungbox
import pandas as pd

# Función para realizar las pruebas Ljung-Box y Dickey-Fuller y retornar los resultados en un diccionario
def pruebas_ljung_box_dickey_fuller(serie, nombre_serie):
    resultados = {}
    
    # Eliminar valores nulos
    serie = serie.dropna()
    
    if len(serie) > 0:
        # Prueba Dickey-Fuller aumentada
        adf_resultado = adfuller(serie)
        resultados['ADF_stat'] = adf_resultado[0]
        resultados['ADF_p_val'] = adf_resultado[1]
        
        # Prueba Ljung-Box
        ljung_box_resultado = acorr_ljungbox(serie, lags=[10], return_df=True)
        resultados['LjungBox_stat'] = ljung_box_resultado['lb_stat'].values[0]
        resultados['LjungBox_p_val'] = ljung_box_resultado['lb_pvalue'].values[0]
        
    else:
        # Si la serie no tiene suficientes datos
        resultados['ADF_stat'] = None
        resultados['ADF_p_val'] = None
        resultados['LjungBox_stat'] = None
        resultados['LjungBox_p_val'] = None
        
    return resultados

# Series de interés
series = ['Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28', 'At']
resultados_pruebas = []

# Realizar las pruebas para cada serie y almacenar los resultados
for serie in series:
    resultados = pruebas_ljung_box_dickey_fuller(df[serie], serie)
    resultados['Serie'] = serie  # Añadir el nombre de la serie
    resultados_pruebas.append(resultados)

# Crear un DataFrame con los resultados
df_resultados = pd.DataFrame(resultados_pruebas)

# Reorganizar las columnas para mayor claridad
df_resultados = df_resultados[['Serie', 'ADF_stat', 'ADF_p_val', 'LjungBox_stat', 'LjungBox_p_val']]

# Mostrar la tabla con todos los resultados
print(df_resultados)

            Serie  ADF_stat     ADF_p_val  LjungBox_stat  LjungBox_p_val
0   Volatilidad_7 -7.461204  5.348106e-11   20281.088500             0.0
1  Volatilidad_14 -6.800477  2.243763e-09   33518.917481             0.0
2  Volatilidad_21 -6.739235  3.149657e-09   39480.766093             0.0
3  Volatilidad_28 -5.342915  4.459348e-06   42274.381698             0.0
4              At -1.617701  4.739347e-01   48959.539109             0.0

Analisis de los resultados de pruebas de estacionaridad

Los resultados de las pruebas de ADF y Ljung-Box que he analizado me brindan información crucial sobre la naturaleza de las series de tiempo que estoy evaluando. En primer lugar, al revisar la prueba ADF, puedo concluir que las series Volatilidad_7, Volatilidad_14, Volatilidad_21 y Volatilidad_28 son estacionarias, ya que sus estadísticos son suficientemente negativos y los p-valores son muy bajos, lo que indica que puedo rechazar la hipótesis nula de que contienen una raíz unitaria.

Sin embargo, la serie At no es estacionaria. Su estadístico ADF es menos negativo y su p-valor es superior a 0.05, lo que significa que no puedo rechazar la hipótesis nula en este caso. Esto sugiere que podría ser necesario aplicar alguna transformación o diferenciar la serie para lograr la estacionariedad, lo cual es fundamental para el análisis de series de tiempo.

Por otro lado, al evaluar los resultados de la prueba de Ljung-Box, encuentro que todas las series, incluso las que son estacionarias, presentan evidencia de autocorrelación en los residuos, ya que los p-valores son prácticamente cero. Esto indica que hay patrones en los datos que no han sido capturados por el análisis hasta ahora. La presencia de autocorrelación sugiere que podría ser útil investigar más a fondo estos datos y considerar ajustes adicionales en mi enfoque para lograr una mejor comprensión de su comportamiento.

A pesar de que las series de volatilidad parecen ser estacionarias según las pruebas ADF, la evidencia de autocorrelación observada en las pruebas ACF me lleva a la decisión de diferenciarlas. En resumen, tengo avances significativos con las series estacionarias, pero la autocorrelación en los residuos me indica que es necesario profundizar en el análisis y ajustar mi enfoque para obtener resultados más precisos y relevantes. Además, debo abordar el tratamiento de la serie At para integrarla adecuadamente en mi evaluación.

Como At no nos dio estacionario, lo diferenciamos y repetimos analisis

import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import acf
from statsmodels.tsa.seasonal import seasonal_decompose
import statsmodels.api as sm

# Aplicar una diferencia a la serie At
df['At_diff'] = df['At'].diff().dropna()

# Graficar la ACF de la serie diferenciada
fig, ax = plt.subplots(figsize=(10, 6))
sm.graphics.tsa.plot_acf(df['At_diff'].dropna(), ax=ax)
plt.title('ACF de At Diferenciada')
plt.show()

# Descomposición de la serie diferenciada
result = seasonal_decompose(df['At_diff'].dropna(), model='additive', period=30)

# Graficar la descomposición
result.plot()
plt.show()

import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import seasonal_decompose
import statsmodels.api as sm

# Lista de las volatilidades a diferenciar
volatilidades = ['Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']

# Bucle para diferenciar, graficar ACF y descomposición de cada volatilidad
for vol in volatilidades:
    # Aplicar la diferenciación
    df[f'{vol}_diff'] = df[vol].diff().dropna()

    # Graficar la ACF de la volatilidad diferenciada
    fig, ax = plt.subplots(figsize=(10, 6))
    sm.graphics.tsa.plot_acf(df[f'{vol}_diff'].dropna(), ax=ax)
    plt.title(f'ACF de {vol} Diferenciada')
    plt.show()

    # Descomposición de la volatilidad diferenciada
    result = seasonal_decompose(df[f'{vol}_diff'].dropna(), model='additive', period=30)

    # Graficar la descomposición
    result.plot()
    plt.suptitle(f'Descomposición de {vol} Diferenciada', y=1.02)
    plt.show()

Decidimos aplicar diferenciación a las series de volatilidad a pesar de que los resultados de la prueba de Dickey-Fuller indicaban que eran estacionarias. La razón detrás de esta decisión fue que la función de autocorrelación (ACF) no mostraba un comportamiento claramente estacionario, lo que nos llevó a cuestionar la estacionariedad de las series.

Aunque el test de Dickey-Fuller sugiere que las series cumplen con los criterios de estacionariedad, la ACF reveló patrones que no eran consistentes con esta conclusión. La ACF puede mostrar la falta de una disminución rápida de la autocorrelación, lo que sugiere que la serie podría tener una estructura más compleja o contener elementos no observados.

Por lo tanto, optamos por diferenciar las series para asegurarnos de que eliminábamos cualquier tendencia o comportamiento no estacionario que pudiera no haber sido captado completamente por la prueba de Dickey-Fuller. Esta decisión nos permite obtener series más adecuadas para análisis posteriores y modelado, asegurando que nuestras inferencias sean más robustas y confiables.

Agregación por grupos (semanas, días, meses) y Cálculo de estadísticas móviles para At y Volatilidades

import pandas as pd



# Columnas de interés (At y volatilidades)
variables = ['At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']

# Agregar por semana
weekly_data = df.resample('W', on='Date').agg({var: ['mean', 'std'] for var in variables})

# Agregar por mes
monthly_data = df.resample('M', on='Date').agg({var: ['mean', 'std'] for var in variables})

# Agregar por día
daily_data = df.resample('D', on='Date').agg({var: ['mean', 'std'] for var in variables})

# Mostrar el resultado
print("Datos semanales (media y desviación estándar):")
print(weekly_data.head())

print("\nDatos mensuales (media y desviación estándar):")
print(monthly_data.head())

print("\nDatos diarios (media y desviación estándar):")
print(daily_data.head())

Datos semanales (media y desviación estándar):
                  At      Volatilidad_7      Volatilidad_14       \
                mean  std          mean  std           mean  std   
Date                                                               
2010-07-18 -4.322978  NaN           0.0  NaN            0.0  NaN   
2010-07-25 -4.322978  0.0           0.0  0.0            0.0  0.0   
2010-08-01 -4.322978  0.0           0.0  0.0            0.0  0.0   
2010-08-08 -4.322978  0.0           0.0  0.0            0.0  0.0   
2010-08-15 -4.322978  0.0           0.0  0.0            0.0  0.0   

           Volatilidad_21      Volatilidad_28       
                     mean  std           mean  std  
Date                                                
2010-07-18            0.0  NaN            0.0  NaN  
2010-07-25            0.0  0.0            0.0  0.0  
2010-08-01            0.0  0.0            0.0  0.0  
2010-08-08            0.0  0.0            0.0  0.0  
2010-08-15            0.0  0.0            0.0  0.0  

Datos mensuales (media y desviación estándar):
                  At           Volatilidad_7           Volatilidad_14  \
                mean       std          mean       std           mean   
Date                                                                    
2010-07-31 -4.322978  0.000000      0.000000  0.000000       0.000000   
2010-08-31 -4.322978  0.000000      0.000000  0.000000       0.000000   
2010-09-30 -4.322978  0.000000      0.000000  0.000000       0.000000   
2010-10-31 -4.226204  0.200805      0.058310  0.087039       0.108616   
2010-11-30 -3.903534  0.242200      0.208736  0.097184       0.204451   

                     Volatilidad_21           Volatilidad_28            
                 std           mean       std           mean       std  
Date                                                                    
2010-07-31  0.000000       0.000000  0.000000       0.000000  0.000000  
2010-08-31  0.000000       0.000000  0.000000       0.000000  0.000000  
2010-09-30  0.000000       0.000000  0.000000       0.009449  0.028832  
2010-10-31  0.087996       0.143952  0.072847       0.163912  0.045570  
2010-11-30  0.033481       0.198878  0.020037       0.207881  0.025490  

Datos diarios (media y desviación estándar):
                  At     Volatilidad_7     Volatilidad_14     Volatilidad_21  \
                mean std          mean std           mean std           mean   
Date                                                                           
2010-07-18 -4.322978 NaN           0.0 NaN            0.0 NaN            0.0   
2010-07-19 -4.322978 NaN           0.0 NaN            0.0 NaN            0.0   
2010-07-20 -4.322978 NaN           0.0 NaN            0.0 NaN            0.0   
2010-07-21 -4.322978 NaN           0.0 NaN            0.0 NaN            0.0   
2010-07-22 -4.322978 NaN           0.0 NaN            0.0 NaN            0.0   

               Volatilidad_28      
           std           mean std  
Date                               
2010-07-18 NaN            0.0 NaN  
2010-07-19 NaN            0.0 NaN  
2010-07-20 NaN            0.0 NaN  
2010-07-21 NaN            0.0 NaN  
2010-07-22 NaN            0.0 NaN  

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_8284\1952300390.py:12: FutureWarning:

'M' is deprecated and will be removed in a future version, please use 'ME' instead.

Media y desviacion standard movil para AT y las volatilidades ( Semanal, Mensual y Anual)

import matplotlib.pyplot as plt

# Lista de variables (At y volatilidades)
variables = ['At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']
colors = ['blue', 'green', 'orange', 'red', 'purple']

# Graficar el comportamiento de la media y desviación estándar por semanas para cada variable
for i, var in enumerate(variables):
    plt.figure(figsize=(10, 6))
    plt.plot(weekly_data.index, weekly_data[var]['mean'], label=f'Media Semanal - {var}', color=colors[i])
    plt.fill_between(weekly_data.index, weekly_data[var]['mean'] - weekly_data[var]['std'],
                     weekly_data[var]['mean'] + weekly_data[var]['std'], color=colors[i], alpha=0.2)
    plt.title(f'Comportamiento de la Media y Desviación Estándar Semanal - {var}')
    plt.xlabel('Fecha')
    plt.ylabel(var)
    plt.legend()
    plt.xticks(rotation=45)
    plt.show()

# Graficar el comportamiento de la media y desviación estándar mensual para cada variable
for i, var in enumerate(variables):
    plt.figure(figsize=(10, 6))
    plt.plot(monthly_data.index, monthly_data[var]['mean'], label=f'Media Mensual - {var}', color=colors[i])
    plt.fill_between(monthly_data.index, monthly_data[var]['mean'] - monthly_data[var]['std'],
                     monthly_data[var]['mean'] + monthly_data[var]['std'], color=colors[i], alpha=0.2)
    plt.title(f'Comportamiento de la Media y Desviación Estándar Mensual - {var}')
    plt.xlabel('Fecha')
    plt.ylabel(var)
    plt.legend()
    plt.xticks(rotation=45)
    plt.show()

# Agregar por año para cada variable
annual_data = df.resample('Y', on='Date').agg({var: ['mean', 'std'] for var in variables})

# Graficar el comportamiento de la media y desviación estándar anual para cada variable
for i, var in enumerate(variables):
    plt.figure(figsize=(10, 6))
    plt.plot(annual_data.index, annual_data[var]['mean'], label=f'Media Anual - {var}', color=colors[i])
    plt.fill_between(annual_data.index, annual_data[var]['mean'] - annual_data[var]['std'],
                     annual_data[var]['mean'] + annual_data[var]['std'], color=colors[i], alpha=0.2)
    plt.title(f'Comportamiento de la Media y Desviación Estándar Anual - {var}')
    plt.xlabel('Fecha')
    plt.ylabel(var)
    plt.legend()
    plt.xticks(rotation=45)
    plt.show()

    import matplotlib.pyplot as plt

# Lista de variables (At y volatilidades)
variables = ['At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']
colors = ['blue', 'green', 'orange', 'red', 'purple']

# Calcular la media móvil y la desviación estándar móvil con una ventana de 30 días para cada variable
for var in variables:
    df[f'Mean_Mobile_{var}'] = df[var].rolling(window=30).mean()
    df[f'Std_Mobile_{var}'] = df[var].rolling(window=30).std()

# Graficar la media móvil y la desviación estándar móvil para cada variable
for i, var in enumerate(variables):
    plt.figure(figsize=(10, 6))
    plt.plot(df['Date'], df[f'Mean_Mobile_{var}'], label=f'Media Móvil (30 días) - {var}', color=colors[i])
    plt.fill_between(df['Date'], 
                     df[f'Mean_Mobile_{var}'] - df[f'Std_Mobile_{var}'],
                     df[f'Mean_Mobile_{var}'] + df[f'Std_Mobile_{var}'], 
                     color=colors[i], alpha=0.2)
    plt.title(f'Media Móvil y Desviación Estándar Móvil (30 días) - {var}')
    plt.xlabel('Fecha')
    plt.ylabel(var)
    plt.legend()
    plt.xticks(rotation=45)
    plt.show()

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_8284\1982343715.py:34: FutureWarning:

'Y' is deprecated and will be removed in a future version, please use 'YE' instead.

Analisis de las medias y desviacion standard del bitcoin

Al observar los gráficos de la desviación estándar y la media de los retornos acumulados y las volatilidades del Bitcoin en horizontes de 7, 14, 21 y 28 días durante los últimos 14 años, me encuentro con patrones interesantes que reflejan la naturaleza volátil y dinámica del mercado de criptomonedas.

El gráfico de la desviación estándar muestra picos significativos en períodos de alta volatilidad, lo que coincide con eventos clave en la historia del Bitcoin, como la adopción institucional, las regulaciones gubernamentales o cambios en la percepción pública. En particular, puedo notar que los horizontes de 7 días tienen desviaciones estándar más altas, indicando que los movimientos a corto plazo son mucho más erráticos y sensibles a cambios repentinos en el mercado. Por otro lado, las desviaciones estándar de 14, 21 y 28 días tienden a ser más suaves, lo que sugiere que la volatilidad se estabiliza un poco a medida que se amplía el horizonte de tiempo.

Al analizar el gráfico de la media de los retornos acumulados, se observa una tendencia creciente en general, lo que indica que, a largo plazo, Bitcoin ha mostrado un desempeño positivo. Sin embargo, también se aprecian algunas caídas significativas en ciertos periodos, como en 2018, cuando el mercado experimentó una corrección importante. Los horizontes de 7 días muestran fluctuaciones más pronunciadas en la media de los retornos, lo que es indicativo de los altibajos típicos del trading en el corto plazo. A medida que el horizonte se amplía a 14, 21 y 28 días, la media de los retornos se vuelve más estable, reflejando una tendencia más clara hacia la recuperación y el crecimiento sostenido.

Comparando ambos gráficos, puedo concluir que existe una relación inversa entre la media de los retornos y la desviación estándar en ciertos momentos. Durante períodos de alta volatilidad, los retornos tienden a ser más inestables, mientras que en períodos de menor volatilidad, los retornos acumulados tienden a ser más positivos y constantes.

Esta visualización me permite reflexionar sobre la importancia de considerar tanto la media como la desviación estándar en la evaluación del rendimiento del Bitcoin. Estos gráficos no solo ilustran la naturaleza riesgosa de invertir en criptomonedas, sino que también resaltan las oportunidades que pueden surgir en medio de la volatilidad, haciendo que la toma de decisiones estratégicas sea esencial para navegar en este entorno de inversión.

Distribucion de frecuencias para diferentes lags

import seaborn as sns

# Lista de variables (At y volatilidades)
variables = ['At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']
colors = ['blue', 'green', 'orange', 'red', 'purple']

# Calcular diferencias con diferentes lags (1 día, 7 días, 30 días) para cada variable
for var in variables:
    df[f'{var}_diff_1'] = df[var].diff(1)   # Lag de 1 día
    df[f'{var}_diff_7'] = df[var].diff(7)   # Lag de 1 semana
    df[f'{var}_diff_30'] = df[var].diff(30) # Lag de 1 mes

# Graficar la distribución de las diferencias para diferentes lags para cada variable
for i, var in enumerate(variables):
    plt.figure(figsize=(10, 6))
    sns.histplot(df[f'{var}_diff_1'].dropna(), label=f'Lag 1 día - {var}', color=colors[i], kde=True)
    sns.histplot(df[f'{var}_diff_7'].dropna(), label=f'Lag 7 días - {var}', color=colors[i], linestyle='--', kde=True)
    sns.histplot(df[f'{var}_diff_30'].dropna(), label=f'Lag 30 días - {var}', color=colors[i], linestyle=':', kde=True)
    plt.title(f'Distribución de Frecuencias para Diferentes Lags - {var}')
    plt.xlabel(f'Diferencias de {var}')
    plt.ylabel('Frecuencia')
    plt.legend()
    plt.show()

Analisis de la distribucion de lags para volatilidad y retornos acumulados del bitcoin

Al examinar las distribuciones de frecuencia de las cuatro volatilidades (Volatilidad_7, Volatilidad_14, Volatilidad_21 y Volatilidad_28) y los retornos acumulados para diferentes lags, noto patrones interesantes que aportan más claridad sobre el comportamiento de estos datos.

En primer lugar, al observar las distribuciones de frecuencia de las volatilidades, todas parecen seguir una distribución normal y presentan formas similares. Esto es alentador, ya que sugiere que las volatilidades se comportan de manera predecible y pueden ser modeladas con técnicas estadísticas que asumen normalidad. Las colas de estas distribuciones son relativamente simétricas y no muestran sesgo significativo, lo que indica una estabilidad en las fluctuaciones de los precios del Bitcoin a lo largo de los horizontes analizados.

Sin embargo, cuando me dirijo a los retornos acumulados, la situación es algo diferente. Al visualizar su distribución de frecuencia, puedo observar que es un poco más ancha en comparación con las de volatilidad. Esto sugiere que los retornos acumulados son más propensos a mostrar extremos, lo que puede indicar que hay una mayor variabilidad en los cambios de precio a lo largo del tiempo. Este ensanchamiento puede ser el resultado de eventos de mercado inusuales o períodos de alta actividad especulativa, que son comunes en el mercado de criptomonedas.

Además, la forma de la distribución de los retornos acumulados no es tan simétrica como la de las volatilidades, lo que puede indicar la presencia de colas más pesadas. Esto significa que, aunque la mayoría de los retornos pueden agruparse alrededor de la media, hay una probabilidad mayor de observar movimientos extremos, ya sean positivos o negativos. Este comportamiento resalta el riesgo asociado con la inversión en Bitcoin, ya que aunque la tendencia general pueda ser positiva, también hay momentos de caída brusca que pueden impactar significativamente el capital invertido.

Medias moviles, retiro de la tendencia y el Ljung box y Dickey fuller test sin tendencia

import matplotlib.pyplot as plt

# Lista de variables (At y volatilidades)
variables = ['At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']
colors = ['blue', 'green', 'orange', 'red', 'purple']

# Calcular medias móviles con diferentes ventanas (2, 3, 4 días) para cada variable
for var in variables:
    df[f'M2_{var}'] = df[var].rolling(window=2).mean()
    df[f'M3_{var}'] = df[var].rolling(window=3).mean()
    df[f'M4_{var}'] = df[var].rolling(window=4).mean()

# Graficar las medias móviles junto con la serie original para cada variable
for i, var in enumerate(variables):
    plt.figure(figsize=(10, 6))
    plt.plot(df['Date'], df[var], label=f'{var} Original', color='black')
    plt.plot(df['Date'], df[f'M2_{var}'], label=f'Media Móvil (2 días) - {var}', color='blue')
    plt.plot(df['Date'], df[f'M3_{var}'], label=f'Media Móvil (3 días) - {var}', color='red')
    plt.plot(df['Date'], df[f'M4_{var}'], label=f'Media Móvil (4 días) - {var}', color='green')
    plt.title(f'Medias Móviles de Diferentes Ventanas - {var}')
    plt.xlabel('Fecha')
    plt.ylabel(var)
    plt.legend()
    plt.xticks(rotation=45)
    plt.show()

# Remover la tendencia restando la media móvil de 4 días de la serie original para cada variable
for i, var in enumerate(variables):
    df[f'Detrended_{var}'] = df[var] - df[f'M4_{var}']

# Graficar la serie sin tendencia para cada variable
for i, var in enumerate(variables):
    plt.figure(figsize=(10, 6))
    plt.plot(df['Date'], df[f'Detrended_{var}'], label=f'Serie sin Tendencia - {var}', color='purple')
    plt.title(f'Serie sin Tendencia (Media Móvil 4 días) - {var}')
    plt.xlabel('Fecha')
    plt.ylabel(f'{var} Detrended')
    plt.legend()
    plt.xticks(rotation=45)
    plt.show()

Analisis de medias movil y serie sin tendencia para volatilidad y retornos acumulados

Al analizar las medias móviles y las series de las volatilidades y los retornos acumulados después de retirarles la tendencia, obtengo una perspectiva más clara sobre el comportamiento subyacente de estas variables a lo largo del tiempo.

Observando las medias móviles de las volatilidades (Volatilidad_7, Volatilidad_14, Volatilidad_21 y Volatilidad_28), noto que estas líneas suavizan las fluctuaciones diarias, permitiéndome identificar patrones con mayor claridad. Las medias móviles muestran una tendencia a la baja en ciertos períodos, lo que indica que la volatilidad del Bitcoin ha disminuido, posiblemente debido a una consolidación del mercado o una menor incertidumbre en el entorno económico. Sin embargo, también se observan picos de volatilidad que correlacionan con eventos de alta actividad en el mercado, como anuncios importantes o cambios regulatorios.

En cuanto a los retornos acumulados, la media móvil también proporciona una perspectiva sobre la tendencia general. Al suavizar los datos, puedo identificar períodos de crecimiento sostenido y momentos de caída. La media móvil revela que, a pesar de la naturaleza volátil de los retornos diarios, hay fases en las que los retornos acumulados tienden a ser positivos y estables, lo que sugiere que, a largo plazo, Bitcoin ha tenido un desempeño sólido.

Cuando analizo las series de volatilidades y retornos acumulados después de retirar la tendencia, me doy cuenta de que ahora puedo centrarme en las fluctuaciones alrededor de la media. Este ajuste me permite observar más claramente los cambios estacionales o cíclicos que podrían haber estado ocultos por la tendencia general. Para las volatilidades, el gráfico muestra que hay oscilaciones regulares, sugiriendo que, a pesar de que la tendencia general podría ser estable, las volatilidades experimentan fluctuaciones significativas en respuesta a cambios en el mercado. Estas variaciones resaltan la naturaleza inherente de los activos volátiles como el Bitcoin.

En el caso de los retornos acumulados, tras retirar la tendencia, la serie muestra una variabilidad más notable, indicando que los retornos pueden tener patrones de comportamiento que no son evidentes al observar la serie original. Este ajuste revela momentos de aumento y disminución abrupta, lo que refuerza la idea de que el mercado puede experimentar episodios de extrema actividad o inactividad, independientemente de la tendencia general.

from statsmodels.tsa.stattools import adfuller
from statsmodels.stats.diagnostic import acorr_ljungbox

# Lista de variables (At y volatilidades)
variables = ['At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']

# Aplicar la prueba de Dickey-Fuller y Ljung-Box para cada variable sin tendencia
for var in variables:
    print(f'\nResultados para {var}:')
    
    # Prueba de Dickey-Fuller en la serie sin tendencia
    adf_result = adfuller(df[f'Detrended_{var}'].dropna())
    print(f'Estadístico ADF: {adf_result[0]}')
    print(f'Valor P: {adf_result[1]}')
    
    # Prueba de Ljung-Box en la serie sin tendencia
    ljungbox_result = acorr_ljungbox(df[f'Detrended_{var}'].dropna(), lags=[10], return_df=True)
    print(ljungbox_result)

Resultados para At:
Estadístico ADF: -10.277894284748266
Valor P: 3.847531979753958e-18
        lb_stat  lb_pvalue
10  1532.556764        0.0

Resultados para Volatilidad_7:
Estadístico ADF: -18.787625910977344
Valor P: 2.0237103913257434e-30
        lb_stat  lb_pvalue
10  4448.710266        0.0

Resultados para Volatilidad_14:
Estadístico ADF: -17.568596257060353
Valor P: 4.062321036340978e-30
        lb_stat  lb_pvalue
10  3833.089277        0.0

Resultados para Volatilidad_21:
Estadístico ADF: -16.209875902476455
Valor P: 3.996632530040086e-29
        lb_stat  lb_pvalue
10  4017.864785        0.0

Resultados para Volatilidad_28:
Estadístico ADF: -16.39354305552273
Valor P: 2.679865846336868e-29
        lb_stat  lb_pvalue
10  4053.593697        0.0

Analisis de los resultados

Al analizar los resultados de las pruebas ADF y Ljung-Box para las variables sin tendencia, obtengo información crucial sobre la estacionariedad y la autocorrelación de estas series.

La serie At presenta un estadístico ADF de -10.28 y un valor P de 3.85e-18, lo que indica que es estacionaria, ya que puedo rechazar la hipótesis nula de que contiene una raíz unitaria. Esto sugiere que la serie se mantiene en torno a una media constante.

En cuanto a las volatilidades, Volatilidad_7 tiene un estadístico ADF de -18.79 y un valor P de 2.02e-30; Volatilidad_14 muestra un estadístico de -17.57 con un valor P de 4.06e-30; Volatilidad_21 tiene un estadístico de -16.21 y un valor P de 3.99e-29; y Volatilidad_28 presenta un estadístico de -16.39 con un valor P de 2.68e-29. Todos estos resultados confirman que las series de volatilidad son también estacionarias.

Sin embargo, los resultados de la prueba de Ljung-Box, que indican estadísticos muy altos y valores P de 0.0 para todas las series, revelan una fuerte presencia de autocorrelación en los residuos. Esto sugiere que, a pesar de la estacionariedad, existen patrones en los datos que no han sido completamente capturados.

En resumen, aunque todas las series son estacionarias, la autocorrelación en los residuos sugiere que debo explorar modelos que puedan capturar estas relaciones temporales, como ARIMA o modelos de suavizado exponencial, para lograr una comprensión más completa de las dinámicas de las series.

Descomposicion para medias moviles de At y volatilidades, luego revisamos Ljung box

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import seasonal_decompose
from statsmodels.stats.diagnostic import acorr_ljungbox

# Lista de variables (At y volatilidades)
variables = ['At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']

# Aplicar media móvil de 7 días y realizar la descomposición para cada variable
for var in variables:
    print(f'\nResultados para {var}:')
    
    # Aplicar media móvil de 7 días para suavizar
    df[f'{var}_MA7'] = df[var].rolling(window=7).mean()

    # Graficar la serie original y la suavizada
    plt.figure(figsize=(10, 6))
    plt.plot(df['Date'], df[var], label=f'{var} Original', color='black')
    plt.plot(df['Date'], df[f'{var}_MA7'], label=f'Media Móvil 7 días - {var}', color='blue')
    plt.title(f'{var} Original vs. Media Móvil (7 días)')
    plt.xlabel('Fecha')
    plt.ylabel(var)
    plt.legend()
    plt.xticks(rotation=45)
    plt.show()

    # Descomposición de la serie temporal
    decomposed = seasonal_decompose(df[f'{var}_MA7'].dropna(), model='additive', period=30)

    # Graficar la descomposición
    decomposed.plot()
    plt.suptitle(f'Descomposición Aditiva - {var}', y=1.02)
    plt.show()

    # Obtener los residuos de la descomposición
    residuos = decomposed.resid.dropna()

    # Aplicar la prueba de Ljung-Box en los residuos
    ljungbox_result = acorr_ljungbox(residuos, lags=[10], return_df=True)

    # Mostrar los resultados de la prueba de Ljung-Box
    print(ljungbox_result)

Resultados para At:

         lb_stat  lb_pvalue
10  14406.772058        0.0

Resultados para Volatilidad_7:

         lb_stat  lb_pvalue
10  15197.793646        0.0

Resultados para Volatilidad_14:

         lb_stat  lb_pvalue
10  16519.537761        0.0

Resultados para Volatilidad_21:

         lb_stat  lb_pvalue
10  17942.086344        0.0

Resultados para Volatilidad_28:

         lb_stat  lb_pvalue
10  16302.266458        0.0

Analisis de las medias moviles y volatilidades para el Bitocin

Al realizar la descomposición de medias móviles para cada variable, obtengo una visión más clara de las tendencias, la estacionalidad y los componentes aleatorios de las series.

Al observar la descomposición de medias móviles de la serie At, identifico que la tendencia es creciente, lo que indica un aumento sostenido en los valores a lo largo del tiempo. A pesar de esta tendencia clara, siempre encontramos picos que reflejan eventos de alta volatilidad o cambios abruptos en el mercado. Esto sugiere que, aunque la serie se comporta de manera predecible en general, aún es sensible a perturbaciones externas.

En la descomposición de Volatilidad_7, se nota una tendencia a la baja en ciertos períodos, pero también se presentan picos de volatilidad, especialmente durante eventos de alta incertidumbre en el mercado. Estos picos resaltan la naturaleza intrínsecamente volátil de esta variable, sugiriendo que, aunque hay períodos de estabilidad, las fluctuaciones pueden ser significativas.

La serie Volatilidad_14 muestra una tendencia similar a la de Volatilidad_7, con una clara reducción de la volatilidad en algunos tramos y picos correspondientes a momentos de alta actividad. Esta descomposición revela que, aunque hay períodos de estabilidad, las fluctuaciones pueden ser pronunciadas en respuesta a eventos específicos del mercado.

Al analizar Volatilidad_21, la tendencia también es descendente, pero con más variaciones que las series anteriores. La descomposición muestra una respuesta más rápida a los cambios en el mercado, evidenciando que la serie podría ser más sensible a eventos externos, reflejando picos que indican respuestas rápidas a situaciones de volatilidad.

Finalmente, en la descomposición de Volatilidad_28, se puede observar una tendencia general menos pronunciada, lo que implica que esta serie podría estar capturando patrones más amplios y menos volátiles en el tiempo. Sin embargo, también presenta fluctuaciones que indican momentos de mayor incertidumbre, mostrando picos que reflejan reacciones a eventos macroeconómicos o cambios significativos en el entorno de las criptomonedas.

Modelos estadisticos

Dividimos en conjunto de entrenamiento, validacion y prediccion

import pandas as pd
import numpy as np
from statsmodels.graphics.tsaplots import plot_acf
import matplotlib.pyplot as plt
from statsmodels.api import qqplot
from statsmodels.tsa.stattools import acf
from statsmodels.stats.diagnostic import normal_ad
from scipy import stats

# Cargar el dataset
df = pd.read_csv(BHdata)

# Convertir la columna 'Date' a tipo datetime
df['Date'] = pd.to_datetime(df['Date'], format='%m/%d/%Y')

# Convertir las columnas 'Price', 'Open', 'High', 'Low' eliminando comas y convirtiendo a float
df['Price'] = pd.to_numeric(df['Price'].str.replace(',', ''), errors='coerce')
df['Open'] = pd.to_numeric(df['Open'].str.replace(',', ''), errors='coerce')
df['High'] = pd.to_numeric(df['High'].str.replace(',', ''), errors='coerce')
df['Low'] = pd.to_numeric(df['Low'].str.replace(',', ''), errors='coerce')

# Convertir la columna 'Vol.' eliminando comas, reemplazando 'K' por 'e3' y 'M' por 'e6', y luego convertir a numérico
df['Vol.'] = df['Vol.'].str.replace('K', 'e3').str.replace('M', 'e6').str.replace(',', '')
df['Vol.'] = pd.to_numeric(df['Vol.'], errors='coerce')

# Convertir la columna 'Change %' eliminando el símbolo '%' y convirtiendo a float
df['Change %'] = df['Change %'].str.replace('%', '').astype(float)

# Eliminar las filas con valores nulos en la columna 'Price'
df.dropna(subset=['Price'], inplace=True)

# Calcular el retorno diario Rt
df['Rt'] = (df['Price'] - df['Price'].shift(1)) / df['Price'].shift(1)

# Calcular el retorno acumulado diario At
df['At'] = df['Rt'].cumsum()

# Función para calcular la volatilidad usando ventanas móviles
def calcular_volatilidad(data, ventana):
    """
    Esta función calcula la volatilidad (desviación estándar) 
    de los retornos diarios utilizando una ventana móvil.
    """
    return data['Rt'].rolling(window=ventana).std()

# Calcular volatilidad para diferentes ventanas
ventanas = [7, 14, 21, 28]
for ventana in ventanas:
    df[f'Volatilidad_{ventana}'] = calcular_volatilidad(df, ventana)

# Mostrar los primeros 10 registros con las nuevas columnas de volatilidad
print(df[['Date', 'At', 'Volatilidad_7', 'Volatilidad_14', 'Volatilidad_21', 'Volatilidad_28']].head(15))

# Dividir los datos en entrenamiento, validación y prueba (últimos 28 datos serán para validación)
train_size = len(df) - 28
test_size = 28
variables = ['Price', 'At', 'Volatilidad_7']

# Crear diccionarios para almacenar los conjuntos de entrenamiento y validación para cada variable
train_data = {}
validation_data = {}

for var in variables:
    train_data[var] = df[var].iloc[:train_size].reset_index(drop=True)  # Resetear los índices
    validation_data[var] = df[var].iloc[-test_size:].reset_index(drop=True)

         Date        At  Volatilidad_7  Volatilidad_14  Volatilidad_21  \
0  2024-03-24       NaN            NaN             NaN             NaN   
1  2024-03-23 -0.047225            NaN             NaN             NaN   
2  2024-03-22 -0.051165            NaN             NaN             NaN   
3  2024-03-21 -0.024226            NaN             NaN             NaN   
4  2024-03-20  0.011652            NaN             NaN             NaN   
5  2024-03-19 -0.073884            NaN             NaN             NaN   
6  2024-03-18  0.015465            NaN             NaN             NaN   
7  2024-03-17  0.027257       0.057142             NaN             NaN   
8  2024-03-16 -0.017734       0.056814             NaN             NaN   
9  2024-03-15  0.045797       0.060785             NaN             NaN   
10 2024-03-14  0.073492       0.060813             NaN             NaN   
11 2024-03-13  0.097009       0.060247             NaN             NaN   
12 2024-03-12  0.075165       0.046199             NaN             NaN   
13 2024-03-11  0.083964       0.035128             NaN             NaN   
14 2024-03-10  0.040492       0.040414         0.04756             NaN   

    Volatilidad_28  
0              NaN  
1              NaN  
2              NaN  
3              NaN  
4              NaN  
5              NaN  
6              NaN  
7              NaN  
8              NaN  
9              NaN  
10             NaN  
11             NaN  
12             NaN  
13             NaN  
14             NaN  

Simple Exponential Smoothing (Sin Librería)

# Función para calcular la suavización exponencial simple (SES)
def SES(y, alpha):
    """
    Realiza la Suavización Exponencial Simple (SES) para una serie temporal 'y' con un factor de suavización 'alpha'.
    Retorna las predicciones suavizadas.
    """
    y_pred = [y[0]]  # Inicializamos la predicción con el primer valor de la serie
    for t in range(1, len(y)):
        y_hat = alpha * y[t-1] + (1 - alpha) * y_pred[t-1]
        y_pred.append(y_hat)
    return y_pred

# Parámetros
alphas = [0.5]  # Factores de suavización que queremos probar
ventanas = [7, 14, 21, 28]  # Ventanas móviles para cada predicción
variables = ['Price', 'Volatilidad_14', 'At']

# Almacenaremos los resultados en un diccionario
predicciones = {}

# Dividimos el conjunto de validación y entrenamiento
train_size = len(df) - 28
test_size = 28

# Para cada variable y cada ventana
for variable in variables:
    predicciones[variable] = {}
    # Tomamos el conjunto de entrenamiento para esa variable
    train_series = df[variable].iloc[:train_size].reset_index(drop=True)
    
    for ventana in ventanas:
        # Inicializar diccionario para cada ventana
        predicciones[variable][ventana] = {}
        
        for alpha in alphas:
            # Aplicar SES sobre la ventana de entrenamiento
            y_train_pred = SES(train_series, alpha)
            
            # Ahora realizamos predicciones para el conjunto de validación (últimos 28 datos)
            val_series = df[variable].iloc[-test_size:].reset_index(drop=True)
            val_predictions = []
            
            # Usamos la última predicción de entrenamiento para empezar a predecir la validación
            last_train_value = y_train_pred[-1]
            
            for i in range(test_size):
                # Predicción para el día siguiente usando SES
                new_val_pred = alpha * val_series.iloc[i] + (1 - alpha) * last_train_value
                val_predictions.append(new_val_pred)
                
                # Actualizamos la última predicción para el siguiente paso
                last_train_value = new_val_pred

            # Guardar las predicciones para esta ventana y alpha
            predicciones[variable][ventana][alpha] = val_predictions

# Imprimir ejemplo de predicciones para verificar
for variable in variables:
    for ventana in ventanas:
        print(f"Predicciones para {variable}, ventana de {ventana} días, alpha={alphas[0]}:")
        print(predicciones[variable][ventana][alphas[0]][:10])  # Mostrar las primeras 10 predicciones
        print("\n")

Predicciones para Price, ventana de 7 días, alpha=0.1:
[np.float64(0.10006349633511052), np.float64(0.10005714670159949), np.float64(0.10005143203143954), np.float64(0.10004628882829558), np.float64(0.10004165994546602), np.float64(0.10003749395091943), np.float64(0.1000337445558275), np.float64(0.10003037010024476), np.float64(0.1000273330902203), np.float64(0.10002459978119826)]


Predicciones para Price, ventana de 14 días, alpha=0.1:
[np.float64(0.10006349633511052), np.float64(0.10005714670159949), np.float64(0.10005143203143954), np.float64(0.10004628882829558), np.float64(0.10004165994546602), np.float64(0.10003749395091943), np.float64(0.1000337445558275), np.float64(0.10003037010024476), np.float64(0.1000273330902203), np.float64(0.10002459978119826)]


Predicciones para Price, ventana de 21 días, alpha=0.1:
[np.float64(0.10006349633511052), np.float64(0.10005714670159949), np.float64(0.10005143203143954), np.float64(0.10004628882829558), np.float64(0.10004165994546602), np.float64(0.10003749395091943), np.float64(0.1000337445558275), np.float64(0.10003037010024476), np.float64(0.1000273330902203), np.float64(0.10002459978119826)]


Predicciones para Price, ventana de 28 días, alpha=0.1:
[np.float64(0.10006349633511052), np.float64(0.10005714670159949), np.float64(0.10005143203143954), np.float64(0.10004628882829558), np.float64(0.10004165994546602), np.float64(0.10003749395091943), np.float64(0.1000337445558275), np.float64(0.10003037010024476), np.float64(0.1000273330902203), np.float64(0.10002459978119826)]


Predicciones para Volatilidad_14, ventana de 7 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]


Predicciones para Volatilidad_14, ventana de 14 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]


Predicciones para Volatilidad_14, ventana de 21 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]


Predicciones para Volatilidad_14, ventana de 28 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]


Predicciones para At, ventana de 7 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]


Predicciones para At, ventana de 14 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]


Predicciones para At, ventana de 21 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]


Predicciones para At, ventana de 28 días, alpha=0.1:
[np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan), np.float64(nan)]

import numpy as np
import pandas as pd
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Simple Exponential Smoothing
def ses_predict(serie, alpha, test_size):
    ses_pred = [serie.iloc[0]]  # Usar el primer valor de la serie

    for t in range(1, len(serie)):
        pred = alpha * serie.iloc[t] + (1 - alpha) * ses_pred[-1]
        ses_pred.append(pred)

    pred_val = []
    for t in range(test_size):
        pred = alpha * df[variable].iloc[len(serie) + t] + (1 - alpha) * ses_pred[-1]
        pred_val.append(pred)

    return pred_val

# Función para evaluar una variable
def evaluar_variable(variable):
    ventanas = [7, 14, 21, 28]
    alphas = [0.5]
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    # Evaluar el SES para la variable
    for ventana in ventanas:
        for alpha in alphas:
            # Serie de tiempo de entrenamiento sin NaNs
            train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

            # Verificar si hay suficientes datos para el entrenamiento
            if len(train_series) < 1:
                print(f"Skipping variable '{variable}' for ventana {ventana} and alpha {alpha} due to insufficient training data.")
                continue

            # Obtener las predicciones para el conjunto de validación
            pred_val = ses_predict(train_series, alpha, test_size)

            # Conjunto de validación real (últimos 28 valores de la serie) sin NaNs
            val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

            # Verificar si hay suficientes datos para la validación
            if len(val_series) < test_size:
                print(f"Skipping variable '{variable}' for ventana {ventana} and alpha {alpha} due to insufficient validation data.")
                continue

            # Calcular las métricas
            mae = mean_absolute_error(val_series, pred_val)
            mse = mean_squared_error(val_series, pred_val)
            rmse = np.sqrt(mse)
            mape = MAPE(val_series, pred_val)
            r2 = r2_score(val_series, pred_val)

            # Guardar los resultados en una lista
            resultados.append({
                'Variable': variable,
                'Ventana': ventana,
                'Alpha': alpha,
                'MAE': mae,
                'MSE': mse,
                'RMSE': rmse,
                'MAPE': mape,
                'R2': r2
            })

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales = pd.concat([evaluar_variable('At'), 
                                 evaluar_variable('Price'), 
                                 evaluar_variable('Volatilidad_14')], 
                                 ignore_index=True)

# Mostrar la tabla con los resultados totales
print(resultados_totales)

          Variable  Ventana  Alpha           MAE           MSE          RMSE  \
0               At        7    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
1               At       14    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
2               At       21    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
3               At       28    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
4            Price        7    0.5  2.211489e+00  4.890684e+00  2.211489e+00   
5            Price       14    0.5  2.211489e+00  4.890684e+00  2.211489e+00   
6            Price       21    0.5  2.211489e+00  4.890684e+00  2.211489e+00   
7            Price       28    0.5  2.211489e+00  4.890684e+00  2.211489e+00   
8   Volatilidad_14        7    0.5  2.161489e+00  4.672035e+00  2.161489e+00   
9   Volatilidad_14       14    0.5  2.161489e+00  4.672035e+00  2.161489e+00   
10  Volatilidad_14       21    0.5  2.161489e+00  4.672035e+00  2.161489e+00   
11  Volatilidad_14       28    0.5  2.161489e+00  4.672035e+00  2.161489e+00   

            MAPE            R2  
0   2.054552e-14  0.000000e+00  
1   2.054552e-14  0.000000e+00  
2   2.054552e-14  0.000000e+00  
3   2.054552e-14  0.000000e+00  
4   2.211489e+03 -2.539388e+34  
5   2.211489e+03 -2.539388e+34  
6   2.211489e+03 -2.539388e+34  
7   2.211489e+03 -2.539388e+34  
8            inf  0.000000e+00  
9            inf  0.000000e+00  
10           inf  0.000000e+00  
11           inf  0.000000e+00  

Variable	Ventana	Alpha	MAE	MSE	RMSE	MAPE	R2
At	7	0.5	8.881784e-16	7.888609e-31	8.881784e-16	2.054552e-14	0.000000e+00
Price	7	0.5	2.211489e+00	4.890684e+00	2.211489e+00	2.211489e+03	-2.539388e+34
Volatilidad_14	7	0.5	2.161489e+00	4.672035e+00	2.161489e+00	inf	0.000000e+00

Al analizar los resultados, se observa que se han calculado diferentes métricas de error (MAE, MSE, RMSE, MAPE y R²) para las variables At, Price y Volatilidad_14 utilizando un método de suavizado exponencial con un parámetro 𝛼 α de 0.5. Sin embargo, es importante destacar que, dado que el suavizado exponencial es una técnica que se utiliza para hacer pronósticos a partir de una serie temporal, el concepto de “ventana” como tal no es aplicable en este contexto.

En el suavizado exponencial, el valor actual se calcula en función de una combinación ponderada del valor observado más reciente y la estimación anterior, lo que permite dar más peso a los datos más recientes. Por esta razón, no se puede establecer un número de ventanas como en otros métodos de suavizado, como las medias móviles, donde se especifica un tamaño de ventana para el cálculo de promedios.

En los resultados, para las variables At y Volatilidad_14, los errores de predicción son extremadamente bajos (en el orden de 1 0 − 16 10 −16 y 1 0 − 30 10 −30 ), lo que sugiere que el modelo se ajusta muy bien a los datos, mientras que para Price, los errores son significativamente mayores, indicando que puede haber más variabilidad en la serie o que el modelo no captura adecuadamente la dinámica de esta variable.

Además, el hecho de que el MAPE sea infinito para las series de volatilidad indica que hay valores en los que el error porcentual no puede calcularse adecuadamente, lo cual puede ser un indicativo de que los datos de entrada tienen características que dificultan el pronóstico preciso.

En resumen, la naturaleza del suavizado exponencial significa que no se puede aplicar el concepto de ventanas de la misma manera que en otros métodos, y los resultados reflejan el rendimiento del modelo en diferentes variables, mostrando un ajuste notablemente bueno para At y Volatilidad_14, mientras que Price presenta un desafío mayor.

Residuos del entrenamiento

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.stats.stattools import jarque_bera

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Simple Exponential Smoothing
def ses_predict(serie, alpha, test_size):
    ses_pred = [serie.iloc[0]]  # Usar el primer valor de la serie

    for t in range(1, len(serie)):
        pred = alpha * serie.iloc[t] + (1 - alpha) * ses_pred[-1]
        ses_pred.append(pred)

    pred_val = []
    for t in range(test_size):
        pred = alpha * serie.iloc[-1] + (1 - alpha) * ses_pred[-1]  # Cambiado para usar el último valor de la serie
        pred_val.append(pred)

    return pred_val

# Función para evaluar la variable y analizar residuos
def evaluar_variable_con_residuos(variable):
    ventanas = [7, 14, 21, 28]
    alphas = [0.5]
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    for ventana in ventanas:
        for alpha in alphas:
            # Serie de tiempo de entrenamiento sin NaNs
            train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

            # Verificar que hay suficientes datos para entrenar
            if len(train_series) < 1:
                print(f"Skipping variable '{variable}' for ventana {ventana} and alpha {alpha} due to insufficient training data.")
                continue

            # Obtener las predicciones para el conjunto de validación
            pred_val = ses_predict(train_series, alpha, test_size)

            # Conjunto de validación real (últimos 28 valores de la serie) sin NaNs
            val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

            # Calcular los residuos
            residuos = train_series - train_series.mean()

            # Calcular métricas
            mae = mean_absolute_error(val_series, pred_val)
            mse = mean_squared_error(val_series, pred_val)
            rmse = np.sqrt(mse)
            mape = MAPE(val_series, pred_val)
            r2 = r2_score(val_series, pred_val)

            # Pruebas de hipótesis
            ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
            ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan
            jarque_bera_results = jarque_bera(residuos)
            jarque_bera_stat = jarque_bera_results[0]
            jarque_bera_pvalue = jarque_bera_results[1]

            # Guardar resultados
            resultados.append({
                'Variable': variable,
                'Ventana': ventana,
                'MAPE': mape,
                'MAE': mae,
                'RMSE': rmse,
                'MSE': mse,
                'R2': r2,
                'Ljung-Box (p-value)': ljung_box_pvalue,
                'Jarque-Bera (p-value)': jarque_bera_pvalue
            })

            # Gráficos
            plt.figure(figsize=(15, 5))

            # Serie de residuos
            plt.subplot(1, 3, 1)
            plt.plot(residuos)
            plt.title(f'Serie de residuos: {variable} (Ventana: {ventana})')
            plt.xlabel('Tiempo')
            plt.ylabel('Residuos')

            # QQPlot
            plt.subplot(1, 3, 2)
            sns.histplot(residuos, kde=True)
            plt.title('Histograma de residuos')

            # ACF
            plt.subplot(1, 3, 3)
            from statsmodels.graphics.tsaplots import plot_acf
            plot_acf(residuos, lags=30, ax=plt.gca())
            plt.title('ACF de residuos')

            plt.tight_layout()
            plt.show()

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales = pd.concat([evaluar_variable_con_residuos('At'), 
                                 evaluar_variable_con_residuos('Price'), 
                                 evaluar_variable_con_residuos('Volatilidad_14')], 
                                 ignore_index=True)

# Mostrar la tabla con los resultados totales
print(resultados_totales)

          Variable  Ventana          MAPE           MAE          RMSE  \
0               At        7  2.054552e-14  8.881784e-16  8.881784e-16   
1               At       14  2.054552e-14  8.881784e-16  8.881784e-16   
2               At       21  2.054552e-14  8.881784e-16  8.881784e-16   
3               At       28  2.054552e-14  8.881784e-16  8.881784e-16   
4            Price        7  0.000000e+00  0.000000e+00  0.000000e+00   
5            Price       14  0.000000e+00  0.000000e+00  0.000000e+00   
6            Price       21  0.000000e+00  0.000000e+00  0.000000e+00   
7            Price       28  0.000000e+00  0.000000e+00  0.000000e+00   
8   Volatilidad_14        7           inf  2.318743e-19  2.318743e-19   
9   Volatilidad_14       14           inf  2.318743e-19  2.318743e-19   
10  Volatilidad_14       21           inf  2.318743e-19  2.318743e-19   
11  Volatilidad_14       28           inf  2.318743e-19  2.318743e-19   

             MSE   R2  Ljung-Box (p-value)  Jarque-Bera (p-value)  
0   7.888609e-31  0.0                  0.0           1.968244e-63  
1   7.888609e-31  0.0                  0.0           1.968244e-63  
2   7.888609e-31  0.0                  0.0           1.968244e-63  
3   7.888609e-31  0.0                  0.0           1.968244e-63  
4   0.000000e+00  1.0                  0.0           0.000000e+00  
5   0.000000e+00  1.0                  0.0           0.000000e+00  
6   0.000000e+00  1.0                  0.0           0.000000e+00  
7   0.000000e+00  1.0                  0.0           0.000000e+00  
8   5.376570e-38  0.0                  0.0           0.000000e+00  
9   5.376570e-38  0.0                  0.0           0.000000e+00  
10  5.376570e-38  0.0                  0.0           0.000000e+00  
11  5.376570e-38  0.0                  0.0           0.000000e+00  

A continuación se presenta la tabla de resultados utilizando suavizado exponencial simple. Se muestra solo una ventana de análisis debido a la naturaleza de este método.

Variable	Ventana	MAPE	MAE	RMSE	MSE	R²	Ljung-Box (p-value)	Jarque-Bera (p-value)
At	7	2.054552e-14	8.881784e-16	8.881784e-16	7.888609e-31	0.0	0.0	1.968244e-63
Price	7	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	1.0	0.0	0.000000e+00
Volatilidad_14	7	inf	2.318743e-19	2.318743e-19	5.376570e-38	0.0	0.0	0.000000e+00

Los resultados presentados en la tabla anterior reflejan el rendimiento de un modelo de suavizado exponencial simple, analizando específicamente los residuos generados por el modelo. Es importante tener en cuenta que estos residuos son la diferencia entre los valores observados y los valores predichos, y su análisis es crucial para evaluar la eficacia del modelo.

Para la variable “At”, observamos que el MAPE (Error Porcentual Absoluto Medio) es de aproximadamente 2.05e-14, lo que indica que los errores de predicción son muy pequeños en términos porcentuales, sugiriendo un buen ajuste del modelo a los datos. El MAE y el RMSE, ambos en el orden de 8.88e-16, son prácticamente cero, lo que sugiere que el modelo predice casi con exactitud los valores observados. Sin embargo, el valor del R² es 0.0, lo que implica que el modelo no explica la variabilidad de los datos, lo cual puede ser un indicativo de que el modelo está sobreajustado o que la serie temporal tiene características que no están siendo capturadas adecuadamente.

En cuanto a la variable “Price”, los errores son igualmente cero, lo que sugiere una predicción perfecta en este caso. Esto es inusual y podría indicar que el modelo está funcionando de manera óptima en este contexto o que los datos no presentan variabilidad en el precio durante el periodo analizado.

Para la variable “Volatilidad_14”, el MAPE muestra un valor infinito, lo que sugiere que hay problemas en la estimación de la predicción; esto puede deberse a que los valores observados son muy cercanos a cero, lo que genera un cálculo poco confiable. Sin embargo, los valores de MAE, RMSE y MSE son todos pequeños (en el orden de 2.32e-19 y 5.38e-38), lo que sugiere que el modelo tiene un bajo nivel de error en la predicción de la volatilidad, aunque esto debe ser interpretado con precaución dado el valor infinito del MAPE.

Los resultados de las pruebas de Ljung-Box y Jarque-Bera son significativos para evaluar la normalidad de los residuos. En este caso, un p-valor de 0.0 en la prueba de Ljung-Box indica que hay autocorrelación en los residuos, lo que puede sugerir que el modelo no está capturando todas las dinámicas de la serie temporal. Por otro lado, el p-valor extremadamente bajo en la prueba de Jarque-Bera (1.97e-63) indica que los residuos no siguen una distribución normal, lo que es una señal de advertencia sobre la validez del modelo.

El análisis de residuos del modelo de suavizado exponencial para las variables de retornos acumulados, precio y volatilidad en los cuatro horizontes temporales (7, 14, 21 y 28 días)

En el caso de los retornos acumulados, la serie de residuos a lo largo del tiempo muestra fluctuaciones significativas, lo cual indica que estos residuos no son completamente aleatorios. Esto sugiere que el modelo no ha capturado toda la estructura subyacente en los datos de retornos acumulados. Además, la distribución de residuos no sigue una normalidad perfecta, presentando asimetrías y varias modas, lo que sugiere que los residuos pueden no estar distribuidos normalmente. Esta falta de normalidad podría limitar la efectividad del modelo en la predicción y ajuste de los datos. Por otro lado, el análisis de la función de autocorrelación de los residuos (ACF) revela valores altos y persistentes, lo cual indica una autocorrelación significativa en los residuos. En un modelo bien ajustado, se esperaría que los residuos no presentaran autocorrelación; por lo tanto, estos resultados sugieren que el modelo de suavizado exponencial podría beneficiarse de ajustes adicionales para capturar mejor las dependencias temporales presentes en los datos.

Para la variable de precio, el análisis de los residuos en el horizonte de 7 días evidencia ciertas limitaciones en el modelo. La serie de residuos muestra una alta volatilidad inicial, que luego disminuye y se estabiliza. Esto sugiere que el modelo no capturó completamente la variabilidad inicial en los precios, aunque los residuos tienden a estabilizarse después de los primeros valores. En cuanto a la distribución de residuos, el histograma revela una alta concentración de valores cerca de cero y una asimetría hacia la izquierda, con algunos valores extremos en ambos lados. Este patrón sugiere una desviación de la normalidad y la presencia de outliers, lo cual podría indicar que el modelo de suavizado exponencial no está capturando adecuadamente las variaciones bruscas en los datos de precios. Además, el ACF de residuos indica una autocorrelación significativa, lo que sugiere que persiste una dependencia en los datos que el modelo no ha logrado captar completamente. Estos patrones en los residuos de precio sugieren que el modelo de suavizado exponencial podría no ser el enfoque más adecuado para capturar la dinámica de esta variable en este horizonte de tiempo; un modelo alternativo, como ARIMA o GARCH, podría mejorar el ajuste al captar mejor tanto la autocorrelación como la volatilidad presentes en la serie de precios.

Finalmente, el análisis de residuos para la volatilidad revela más indicios de las limitaciones del modelo de suavizado exponencial. La serie de residuos presenta fluctuaciones constantes con picos esporádicos que aumentan hacia el final del periodo, lo cual indica que el modelo presenta dificultades para capturar completamente la variabilidad de la volatilidad, especialmente en los momentos de mayor incremento. Esto sugiere una posible subestimación de algunos valores extremos en la serie de volatilidad. La distribución de residuos también refleja un sesgo hacia la derecha, con una alta concentración de valores alrededor de cero y algunos valores extremos positivos. Este patrón indica que los residuos no siguen una distribución normal y que existen ciertos valores anómalos, lo cual podría sugerir que el modelo no está capturando adecuadamente todos los patrones presentes en los datos de volatilidad. Además, el ACF de residuos muestra una alta correlación positiva en los primeros lags, que disminuye lentamente, lo que indica una estructura de dependencia temporal que el modelo no ha capturado del todo. Esto podría limitar su capacidad para realizar predicciones precisas en el contexto de volatilidad.

Residuos de la prediccion

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Simple Exponential Smoothing
def ses_predict(serie, alpha, test_size):
    ses_pred = [serie.iloc[0]]  # Usar el primer valor de la serie

    for t in range(1, len(serie)):
        pred = alpha * serie.iloc[t] + (1 - alpha) * ses_pred[-1]
        ses_pred.append(pred)

    pred_val = []
    for t in range(test_size):
        pred = alpha * serie.iloc[-1] + (1 - alpha) * ses_pred[-1]  # Cambiado para usar el último valor de la serie
        pred_val.append(pred)

    return pred_val

# Función para evaluar el modelo en el conjunto de test y analizar residuos
def evaluar_modelo_en_conjunto_test(variable, alpha, test_size):
    train_size = len(df) - test_size
    # Serie de tiempo de entrenamiento sin NaNs
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    # Verificar que hay suficientes datos para entrenar
    if len(train_series) < 1:
        print(f"Insufficient training data for variable '{variable}'.")
        return None

    # Obtener las predicciones para el conjunto de validación
    pred_val = ses_predict(train_series, alpha, test_size)

    # Conjunto de validación real (últimos test_size valores de la serie) sin NaNs
    val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

    # Calcular los residuos
    residuos = val_series - pred_val

    # Calcular métricas
    mae = mean_absolute_error(val_series, pred_val)
    mse = mean_squared_error(val_series, pred_val)
    rmse = np.sqrt(mse)
    mape = MAPE(val_series, pred_val)
    r2 = r2_score(val_series, pred_val)

    # Prueba de Ljung-Box
    ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
    ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan

    # Guardar resultados
    return {
        'Variable': variable,
        'MAPE': mape,
        'MAE': mae,
        'RMSE': rmse,
        'MSE': mse,
        'R2': r2,
        'Ljung-Box (p-value)': ljung_box_pvalue
    }

# Variables y parámetros a evaluar
variables = ['At', 'Price', 'Volatilidad_14']
alpha = 0.5
test_size = 28

# Evaluar cada variable y almacenar los resultados
resultados = []

for variable in variables:
    resultado = evaluar_modelo_en_conjunto_test(variable, alpha, test_size)
    if resultado is not None:
        resultados.append(resultado)

# Convertir los resultados en un DataFrame
resultados_df = pd.DataFrame(resultados)

# Mostrar la tabla con los resultados
print(resultados_df)

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\stattools.py:702: RuntimeWarning:

invalid value encountered in divide

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\stattools.py:702: RuntimeWarning:

invalid value encountered in divide

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\stattools.py:702: RuntimeWarning:

invalid value encountered in divide

         Variable          MAPE           MAE          RMSE           MSE  \
0              At  2.054552e-14  8.881784e-16  8.881784e-16  7.888609e-31   
1           Price  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00   
2  Volatilidad_14           inf  2.318743e-19  2.318743e-19  5.376570e-38   

    R2  Ljung-Box (p-value)  
0  0.0                  NaN  
1  1.0                  NaN  
2  0.0                  NaN  

Variable	MAPE	MAE	RMSE	MSE	R²	Ljung-Box (p-value)
At	2.054552e-14	8.881784e-16	8.881784e-16	7.888609e-31	0.0	NaN
Price	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	1.0	NaN
Volatilidad_14	inf	2.318743e-19	2.318743e-19	5.376570e-38	0.0	NaN

Para la variable “At”, el MAPE es de aproximadamente 2.05e-14, lo que indica que los errores porcentuales son mínimos y sugiere un buen ajuste del modelo. Los valores de MAE y RMSE son extremadamente bajos (8.88e-16), lo que sugiere que las predicciones se acercan de manera precisa a los valores reales. Además, el MSE de 7.89e-31 refuerza la idea de un ajuste preciso. Sin embargo, el R² de 0.0 indica que el modelo no explica ninguna variabilidad de los datos, lo que puede ser preocupante y sugiere que el modelo puede no estar capturando adecuadamente las dinámicas subyacentes de la serie temporal.

En cuanto a la variable “Price”, todos los valores de MAPE, MAE, RMSE y MSE son cero, lo que sugiere que el modelo predice perfectamente los precios. Este resultado es atípico y podría implicar que el precio es constante a lo largo del tiempo en el conjunto de datos analizado, o que el modelo ha sido ajustado de manera perfecta a los datos sin capturar variabilidad. El R² de 1.0 refuerza la hipótesis anterior de que el modelo ha hecho una predicción exacta.

Para la variable “Volatilidad_14”, el MAPE muestra un valor infinito, lo que indica que la variabilidad de los valores observados es demasiado pequeña en comparación con los errores de predicción, sugiriendo que el modelo no es confiable para esta variable. Aunque los valores de MAE, RMSE y MSE son bajos (en el orden de 2.32e-19 y 5.38e-38), la interpretación se ve afectada por el MAPE infinito, que sugiere una falta de variabilidad en los datos de volatilidad. Además, el R² de 0.0 implica que el modelo no explica la variabilidad de la volatilidad observada, sugiriendo que se necesitan ajustes significativos o un enfoque diferente para esta variable.

Simple Exponential Smoothing (Usando statsmodels.tsa.holtwinters)

import pandas as pd
import numpy as np
from statsmodels.tsa.holtwinters import SimpleExpSmoothing
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox

# Parámetros
alphas = [0.5]  # Factores de suavización que queremos probar
ventanas = [7, 14, 21, 28]  # Ventanas móviles para cada predicción
variables = ['Price', 'Volatilidad_14', 'At']

# Almacenaremos las predicciones
predicciones = {}

# Dividimos el conjunto de validación y entrenamiento
train_size = len(df) - 28
test_size = 28

# Para cada variable y cada ventana
for variable in variables:
    predicciones[variable] = {}
    # Tomamos el conjunto de entrenamiento para esa variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    for ventana in ventanas:
        # Inicializar diccionario para cada ventana
        predicciones[variable][ventana] = {}

        for alpha in alphas:
            # Aplicar SES usando SimpleExpSmoothing de statsmodels
            model = SimpleExpSmoothing(train_series)
            model_fit = model.fit(smoothing_level=alpha, optimized=False)  # 'optimized=False' para usar el alpha específico
            y_train_pred = model_fit.fittedvalues

            # Ahora realizamos predicciones para el conjunto de validación (últimos test_size datos)
            val_predictions = model_fit.forecast(test_size)

            # Guardar las predicciones para esta ventana y alpha
            predicciones[variable][ventana][alpha] = val_predictions

import numpy as np
import pandas as pd
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.tsa.holtwinters import SimpleExpSmoothing

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Simple Exponential Smoothing
def ses_predict(serie, alpha, test_size):
    model = SimpleExpSmoothing(serie)
    model_fit = model.fit(smoothing_level=alpha, optimized=False)
    
    # Predicciones para el conjunto de validación
    pred_val = model_fit.forecast(test_size)
    
    return pred_val

# Función para evaluar una variable
def evaluar_variable(variable):
    ventanas = [7, 14, 21, 28]
    alphas = [0.5]
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    # Evaluar el SES para la variable
    for ventana in ventanas:
        for alpha in alphas:
            # Serie de tiempo de entrenamiento sin NaNs
            train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

            # Verificar si hay suficientes datos para el entrenamiento
            if len(train_series) < 1:
                print(f"Skipping variable '{variable}' for ventana {ventana} and alpha {alpha} due to insufficient training data.")
                continue

            # Obtener las predicciones para el conjunto de validación
            pred_val = ses_predict(train_series, alpha, test_size)

            # Conjunto de validación real (últimos 28 valores de la serie) sin NaNs
            val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

            # Verificar si hay suficientes datos para la validación
            if len(val_series) < test_size:
                print(f"Skipping variable '{variable}' for ventana {ventana} and alpha {alpha} due to insufficient validation data.")
                continue

            # Calcular las métricas
            mae = mean_absolute_error(val_series, pred_val)
            mse = mean_squared_error(val_series, pred_val)
            rmse = np.sqrt(mse)
            mape = MAPE(val_series, pred_val)
            r2 = r2_score(val_series, pred_val)

            # Guardar los resultados en una lista
            resultados.append({
                'Variable': variable,
                'Ventana': ventana,
                'Alpha': alpha,
                'MAE': mae,
                'MSE': mse,
                'RMSE': rmse,
                'MAPE': mape,
                'R2': r2
            })

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales = pd.concat([evaluar_variable('At'), 
                                 evaluar_variable('Price'), 
                                 evaluar_variable('Volatilidad_14')], 
                                 ignore_index=True)

# Mostrar la tabla con los resultados totales
print(resultados_totales)

          Variable  Ventana  Alpha           MAE           MSE          RMSE  \
0               At        7    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
1               At       14    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
2               At       21    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
3               At       28    0.5  8.881784e-16  7.888609e-31  8.881784e-16   
4            Price        7    0.5  0.000000e+00  0.000000e+00  0.000000e+00   
5            Price       14    0.5  0.000000e+00  0.000000e+00  0.000000e+00   
6            Price       21    0.5  0.000000e+00  0.000000e+00  0.000000e+00   
7            Price       28    0.5  0.000000e+00  0.000000e+00  0.000000e+00   
8   Volatilidad_14        7    0.5  4.637486e-19  2.150628e-37  4.637486e-19   
9   Volatilidad_14       14    0.5  4.637486e-19  2.150628e-37  4.637486e-19   
10  Volatilidad_14       21    0.5  4.637486e-19  2.150628e-37  4.637486e-19   
11  Volatilidad_14       28    0.5  4.637486e-19  2.150628e-37  4.637486e-19   

    MAPE   R2  
0    NaN  0.0  
1    NaN  0.0  
2    NaN  0.0  
3    NaN  0.0  
4    NaN  1.0  
5    NaN  1.0  
6    NaN  1.0  
7    NaN  1.0  
8    NaN  0.0  
9    NaN  0.0  
10   NaN  0.0  
11   NaN  0.0  

A continuación se presenta la tabla de resultados utilizando suavizado exponencial simple, donde se muestra solo una ventana de análisis por la naturaleza del método.

Variable	Ventana	Alpha	MAE	MSE	RMSE	MAPE	R2
At	7	0.5	8.881784e-16	7.888609e-31	8.881784e-16	NaN	0.0
Price	7	0.5	0.000000e+00	0.000000e+00	0.000000e+00	NaN	1.0
Volatilidad_14	7	0.5	4.637486e-19	2.150628e-37	4.637486e-19	NaN	0.0

Los resultados obtenidos a partir del análisis utilizando suavizado exponencial simple se presentan en la tabla anterior, donde se incluye solo una ventana de análisis debido a la naturaleza de este método. Se observa que, para la variable “At” en una ventana de 7 días y con un valor de alpha de 0.5, el error absoluto medio (MAE) es de aproximadamente 8.88e-16, mientras que el error cuadrático medio (MSE) y la raíz del error cuadrático medio (RMSE) son ambos 7.89e-31 y 8.88e-16, respectivamente. Estos valores indican una precisión notable en la predicción, aunque el MAE y el RMSE son prácticamente cero, lo que sugiere que el modelo se ajusta muy bien a los datos.

En el caso de la variable “Price”, los resultados son igualmente satisfactorios, con un MAE, MSE y RMSE de cero. Esto sugiere que el modelo no presenta errores en las predicciones, lo que indica una capacidad excepcional para estimar el precio a partir de los datos proporcionados.

Para la variable “Volatilidad_14”, aunque se mantiene el mismo MAE que para “At”, con un valor de 4.64e-19, el MSE es extremadamente bajo, 2.15e-37, lo que implica una buena consistencia en las predicciones. Sin embargo, el valor de R² para esta variable es 0.0, lo que sugiere que el modelo no explica variabilidad en los datos observados.

En resumen, los resultados muestran un rendimiento destacado del modelo de suavizado exponencial simple para las variables “At” y “Price”, indicando que este enfoque es adecuado para el análisis de series temporales en este contexto. Sin embargo, la baja capacidad explicativa del modelo para la volatilidad señala la necesidad de considerar métodos adicionales o variables explicativas que puedan mejorar la precisión en futuras evaluaciones.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.stats.stattools import jarque_bera
from statsmodels.tsa.holtwinters import SimpleExpSmoothing
import statsmodels.api as sm

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Simple Exponential Smoothing
def ses_predict(serie, alpha, test_size):
    model = SimpleExpSmoothing(serie)
    model_fit = model.fit(smoothing_level=alpha, optimized=False)
    pred_val = model_fit.forecast(test_size)
    return pred_val, model_fit.resid  # Retornar también los residuos

# Función para evaluar la variable y analizar residuos
def evaluar_variable_con_residuos(variable):
    alphas = [0.5]
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    for alpha in alphas:
        # Serie de tiempo de entrenamiento sin NaNs
        train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

        # Verificar que hay suficientes datos para entrenar
        if len(train_series) < 1:
            print(f"Skipping variable '{variable}' due to insufficient training data.")
            continue

        # Obtener las predicciones y residuos para el conjunto de validación
        pred_val, residuos = ses_predict(train_series, alpha, test_size)

        # Conjunto de validación real (últimos 28 valores de la serie) sin NaNs
        val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

        # Calcular métricas
        mae = mean_absolute_error(val_series, pred_val)
        mse = mean_squared_error(val_series, pred_val)
        rmse = np.sqrt(mse)
        mape = MAPE(val_series, pred_val)
        r2 = r2_score(val_series, pred_val)

        # Pruebas de hipótesis
        ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
        ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan
        jarque_bera_results = jarque_bera(residuos)
        jarque_bera_stat = jarque_bera_results[0]
        jarque_bera_pvalue = jarque_bera_results[1]

        # Guardar resultados
        resultados.append({
            'Variable': variable,
            'MAPE': mape,
            'MAE': mae,
            'RMSE': rmse,
            'MSE': mse,
            'R2': r2,
            'Ljung-Box (p-value)': ljung_box_pvalue,
            'Jarque-Bera (p-value)': jarque_bera_pvalue
        })

        # Gráficos
        plt.figure(figsize=(15, 5))

        # Serie de residuos
        plt.subplot(1, 3, 1)
        plt.plot(residuos)
        plt.title(f'Serie de residuos: {variable}')
        plt.xlabel('Tiempo')
        plt.ylabel('Residuos')

        # QQPlot
        plt.subplot(1, 3, 2)
        sm.qqplot(residuos, line='s', ax=plt.gca())
        plt.title('QQPlot de residuos')

        # ACF
        plt.subplot(1, 3, 3)
        from statsmodels.graphics.tsaplots import plot_acf
        plot_acf(residuos, lags=30, ax=plt.gca())
        plt.title('ACF de residuos')

        plt.tight_layout()
        plt.show()

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales = pd.concat([evaluar_variable_con_residuos('At'), 
                                 evaluar_variable_con_residuos('Price'), 
                                 evaluar_variable_con_residuos('Volatilidad_14')], 
                                 ignore_index=True)

# Mostrar la tabla con los resultados totales
print(resultados_totales)

         Variable  MAPE           MAE          RMSE           MSE   R2  \
0              At   NaN  8.881784e-16  8.881784e-16  7.888609e-31  0.0   
1           Price   NaN  0.000000e+00  0.000000e+00  0.000000e+00  1.0   
2  Volatilidad_14   NaN  4.637486e-19  4.637486e-19  2.150628e-37  0.0   

   Ljung-Box (p-value)  Jarque-Bera (p-value)  
0        6.386049e-299                    0.0  
1         0.000000e+00                    0.0  
2         0.000000e+00                    0.0  

El análisis de los residuos generados por el modelo de suavizado exponencial, implementado a través de la librería statsmodels, para las variables de retornos acumulados, precio y volatilidad en los cuatro horizontes temporales (7, 14, 21 y 28 días)

Para la variable de retornos acumulados, la distribución de residuos en el tiempo muestra una estabilidad notable a lo largo del gráfico, con algunos picos ocasionales, pero manteniéndose generalmente entre 2.5 y -2.5. Este comportamiento indica que los residuos son relativamente estables, con solo algunos valores extremos que no afectan en gran medida la consistencia de los residuos. En el QQ plot, los residuos presentan una distribución normal en el centro, aunque se desvían levemente en las esquinas, lo que sugiere ligeras desviaciones de normalidad en los extremos. Finalmente, la prueba ACF muestra pocos residuos fuera de la banda de significancia y una estructura de autocorrelación en forma de espina descendente, lo cual sugiere que existe cierta dependencia temporal, aunque es mínima y en general parece un modelo razonablemente ajustado para esta variable.

En cuanto a la variable de precio, la distribución de residuos en el tiempo evidencia residuos grandes al inicio del gráfico, que se reducen considerablemente hacia el final. Esto sugiere que el modelo tiene dificultades para capturar la variabilidad inicial en los precios, aunque logra un ajuste más preciso en los valores recientes. El QQ plot revela una clara desviación de la normalidad, con puntos fuera de la línea central, especialmente en el centro de la distribución. Esta desviación indica que los residuos de precio no siguen una distribución normal y podrían estar afectados por factores externos o fluctuaciones significativas en los datos de entrada. La ACF de los residuos muestra algunos valores por fuera de la banda de significancia, con una estructura de espina descendente, lo que sugiere que, aunque hay algunas dependencias en los datos, la mayoría de los residuos son independientes en el tiempo. No obstante, los residuos iniciales grandes y la no normalidad indican que el modelo de suavizado exponencial podría no ser el mejor para capturar la dinámica de precio en esta variable.

Finalmente, en el caso de la volatilidad, la distribución de residuos es relativamente estable a lo largo del tiempo, aunque muestra un ligero crecimiento hacia el final del periodo. Esta estabilidad en los residuos, con solo un pequeño aumento final, sugiere que el modelo de suavizado exponencial se ajusta de manera aceptable, aunque puede estar subestimando ciertos valores hacia el final del horizonte temporal. El QQ plot de los residuos muestra una distribución normal en el centro, con desviaciones leves en las esquinas, indicando que, en general, los residuos siguen una distribución normal, aunque con algunos valores atípicos en los extremos. La ACF presenta pocos residuos fuera de la banda de significancia y una estructura en espina descendente, lo cual sugiere que, aunque hay pequeñas dependencias en los datos, el modelo captura adecuadamente la mayoría de las características de la volatilidad.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.tsa.holtwinters import SimpleExpSmoothing

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Simple Exponential Smoothing
def ses_predict(serie, alpha, test_size):
    model = SimpleExpSmoothing(serie)
    model_fit = model.fit(smoothing_level=alpha, optimized=False)
    pred_val = model_fit.forecast(test_size)
    return pred_val, model_fit.resid  # Retornar también los residuos

# Función para evaluar el modelo en el conjunto de prueba
def evaluar_modelo_en_test(variable):
    alphas = [0.5]
    train_size = len(df) - 28  # Tamaño del conjunto de entrenamiento
    test_size = 28               # Tamaño del conjunto de prueba

    resultados = []

    for alpha in alphas:
        # Serie de tiempo de entrenamiento sin NaNs
        train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

        # Obtener las predicciones y residuos para el conjunto de prueba
        pred_val, residuos = ses_predict(train_series, alpha, test_size)

        # Conjunto de prueba real (últimos 28 valores de la serie) sin NaNs
        val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

        # Calcular métricas
        mae = mean_absolute_error(val_series, pred_val)
        mse = mean_squared_error(val_series, pred_val)
        rmse = np.sqrt(mse)
        mape = MAPE(val_series, pred_val)
        r2 = r2_score(val_series, pred_val)

        # Pruebas de hipótesis
        ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
        ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan

        # Guardar resultados
        resultados.append({
            'Variable': variable,
            'MAPE': mape,
            'MAE': mae,
            'RMSE': rmse,
            'MSE': mse,
            'R2': r2,
            'Ljung-Box (p-value)': ljung_box_pvalue
        })

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales_test = pd.concat([evaluar_modelo_en_test('At'), 
                                      evaluar_modelo_en_test('Price'), 
                                      evaluar_modelo_en_test('Volatilidad_14')], 
                                     ignore_index=True)

# Mostrar la tabla con los resultados totales del conjunto de prueba
print(resultados_totales_test)

         Variable  MAPE           MAE          RMSE           MSE   R2  \
0              At   NaN  8.881784e-16  8.881784e-16  7.888609e-31  0.0   
1           Price   NaN  0.000000e+00  0.000000e+00  0.000000e+00  1.0   
2  Volatilidad_14   NaN  4.637486e-19  4.637486e-19  2.150628e-37  0.0   

   Ljung-Box (p-value)  
0        6.386049e-299  
1         0.000000e+00  
2         0.000000e+00  

Variable	MAPE	MAE	RMSE	MSE	R²	Ljung-Box (p-value)
At	NaN	8.881784e-16	8.881784e-16	7.888609e-31	0.0	6.386049e-299
Price	NaN	0.000000e+00	0.000000e+00	0.000000e+00	1.0	0.000000e+00
Volatilidad_14	NaN	4.637486e-19	4.637486e-19	2.150628e-37	0.0	0.000000e+00

Para la variable “At”, los valores de MAE (8.88e-16) y RMSE (8.88e-16) son extremadamente bajos, lo que sugiere que las predicciones están muy cerca de los valores reales. Sin embargo, el MAPE es NaN, lo que implica que no hay variabilidad en los datos para calcular este error porcentual. El MSE también es muy pequeño (7.89e-31), indicando que los errores de predicción son mínimos. El R² de 0.0 sugiere que el modelo no explica la variabilidad de la serie temporal, lo que podría ser un indicativo de que el modelo es demasiado simple para capturar las dinámicas de la serie. Además, el p-valor de Ljung-Box (6.39e-299) indica que los residuos son independientes, lo cual es un buen signo para la validez del modelo.

En el caso de “Price”, los resultados muestran una predicción perfecta, con MAE, RMSE y MSE todos igual a cero. Esto sugiere que el modelo ha logrado ajustarse completamente a los datos, probablemente porque el precio es constante a lo largo del tiempo. El R² de 1.0 refuerza esta idea, indicando que el modelo explica el 100% de la variabilidad. Sin embargo, este ajuste perfecto también puede ser un indicativo de sobreajuste, donde el modelo ha capturado ruidos en lugar de patrones útiles. El p-valor de Ljung-Box es 0, lo que implica que hay autocorrelación en los residuos, lo que podría ser un indicativo de que el modelo no ha capturado completamente la estructura temporal de los datos.

Para la variable “Volatilidad_14”, aunque los errores de MAE y RMSE son muy bajos (4.64e-19), el MAPE es NaN, lo que sugiere que, al igual que en el caso de “At”, no hay suficiente variabilidad para calcularlo. El MSE es también bajo (2.15e-37), indicando que los errores de predicción son pequeños. Sin embargo, el R² de 0.0 sugiere que el modelo no explica la variabilidad de esta variable, lo que puede señalar que se necesita un modelo más complejo o diferente para capturar adecuadamente las dinámicas de la volatilidad. El p-valor de Ljung-Box (0) sugiere que los residuos no son independientes, lo que puede ser motivo de preocupación y sugiere que el modelo podría mejorarse.

Doble suavizado exponencial sin libreria

import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox

# Parámetros
alphas = [0.5]  # Factores de suavización que queremos probar
ventanas = [7, 14, 21, 28]  # Ventanas móviles para cada predicción
variables = ['Price', 'Volatilidad_14', 'At']

# Función para realizar Double Exponential Smoothing
def double_exponential_smoothing(series, alpha, beta, n_forecast):
    level = series[0]
    trend = series[1] - series[0]  # Inicializar tendencia
    result = [level + trend]  # Primer pronóstico

    # Lista para almacenar los valores de nivel y tendencia
    levels = [level]
    trends = [trend]

    # Suavizado
    for t in range(1, len(series)):
        last_level = level
        level = alpha * series[t] + (1 - alpha) * (last_level + trend)
        trend = beta * (level - last_level) + (1 - beta) * trend

        levels.append(level)
        trends.append(trend)

        # Pronóstico
        if t >= len(series) - 1:
            forecast = level + trend
            result.append(forecast)

    # Pronósticos para los próximos n períodos
    forecasts = []
    for i in range(n_forecast):
        forecast = level + (i + 1) * trend
        forecasts.append(forecast)

    return forecasts, result, levels, trends

# Almacenaremos las predicciones
predicciones = {}

# Dividimos el conjunto de validación y entrenamiento
train_size = len(df) - 28
test_size = 28

# Para cada variable y cada ventana
for variable in variables:
    predicciones[variable] = {}
    # Tomamos el conjunto de entrenamiento para esa variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    for ventana in ventanas:
        # Inicializar diccionario para cada ventana
        predicciones[variable][ventana] = {}

        for alpha in alphas:
            # Definir un beta (puedes experimentar con este valor)
            beta = 0.5  

            # Aplicar Double Exponential Smoothing
            val_predictions, y_train_pred, levels, trends = double_exponential_smoothing(train_series.values, alpha, beta, test_size)

            # Guardar las predicciones para esta ventana y alpha
            predicciones[variable][ventana][alpha] = val_predictions

# Mostrar predicciones
for variable in predicciones:
    for ventana in predicciones[variable]:
        print(f"Predicciones para {variable} con ventana {ventana}: {predicciones[variable][ventana]}")

Predicciones para Price con ventana 7: {0.5: [np.float64(0.0999999999994), np.float64(0.09999999999986978), np.float64(0.10000000000033957), np.float64(0.10000000000080936), np.float64(0.10000000000127914), np.float64(0.10000000000174893), np.float64(0.10000000000221872), np.float64(0.1000000000026885), np.float64(0.10000000000315828), np.float64(0.10000000000362808), np.float64(0.10000000000409785), np.float64(0.10000000000456764), np.float64(0.10000000000503743), np.float64(0.10000000000550721), np.float64(0.100000000005977), np.float64(0.1000000000064468), np.float64(0.10000000000691657), np.float64(0.10000000000738636), np.float64(0.10000000000785615), np.float64(0.10000000000832593), np.float64(0.10000000000879572), np.float64(0.10000000000926551), np.float64(0.10000000000973529), np.float64(0.10000000001020508), np.float64(0.10000000001067487), np.float64(0.10000000001114465), np.float64(0.10000000001161444), np.float64(0.10000000001208423)]}
Predicciones para Price con ventana 14: {0.5: [np.float64(0.0999999999994), np.float64(0.09999999999986978), np.float64(0.10000000000033957), np.float64(0.10000000000080936), np.float64(0.10000000000127914), np.float64(0.10000000000174893), np.float64(0.10000000000221872), np.float64(0.1000000000026885), np.float64(0.10000000000315828), np.float64(0.10000000000362808), np.float64(0.10000000000409785), np.float64(0.10000000000456764), np.float64(0.10000000000503743), np.float64(0.10000000000550721), np.float64(0.100000000005977), np.float64(0.1000000000064468), np.float64(0.10000000000691657), np.float64(0.10000000000738636), np.float64(0.10000000000785615), np.float64(0.10000000000832593), np.float64(0.10000000000879572), np.float64(0.10000000000926551), np.float64(0.10000000000973529), np.float64(0.10000000001020508), np.float64(0.10000000001067487), np.float64(0.10000000001114465), np.float64(0.10000000001161444), np.float64(0.10000000001208423)]}
Predicciones para Price con ventana 21: {0.5: [np.float64(0.0999999999994), np.float64(0.09999999999986978), np.float64(0.10000000000033957), np.float64(0.10000000000080936), np.float64(0.10000000000127914), np.float64(0.10000000000174893), np.float64(0.10000000000221872), np.float64(0.1000000000026885), np.float64(0.10000000000315828), np.float64(0.10000000000362808), np.float64(0.10000000000409785), np.float64(0.10000000000456764), np.float64(0.10000000000503743), np.float64(0.10000000000550721), np.float64(0.100000000005977), np.float64(0.1000000000064468), np.float64(0.10000000000691657), np.float64(0.10000000000738636), np.float64(0.10000000000785615), np.float64(0.10000000000832593), np.float64(0.10000000000879572), np.float64(0.10000000000926551), np.float64(0.10000000000973529), np.float64(0.10000000001020508), np.float64(0.10000000001067487), np.float64(0.10000000001114465), np.float64(0.10000000001161444), np.float64(0.10000000001208423)]}
Predicciones para Price con ventana 28: {0.5: [np.float64(0.0999999999994), np.float64(0.09999999999986978), np.float64(0.10000000000033957), np.float64(0.10000000000080936), np.float64(0.10000000000127914), np.float64(0.10000000000174893), np.float64(0.10000000000221872), np.float64(0.1000000000026885), np.float64(0.10000000000315828), np.float64(0.10000000000362808), np.float64(0.10000000000409785), np.float64(0.10000000000456764), np.float64(0.10000000000503743), np.float64(0.10000000000550721), np.float64(0.100000000005977), np.float64(0.1000000000064468), np.float64(0.10000000000691657), np.float64(0.10000000000738636), np.float64(0.10000000000785615), np.float64(0.10000000000832593), np.float64(0.10000000000879572), np.float64(0.10000000000926551), np.float64(0.10000000000973529), np.float64(0.10000000001020508), np.float64(0.10000000001067487), np.float64(0.10000000001114465), np.float64(0.10000000001161444), np.float64(0.10000000001208423)]}
Predicciones para Volatilidad_14 con ventana 7: {0.5: [np.float64(-2.655992905380553e-10), np.float64(-2.758814620939934e-10), np.float64(-2.8616363364993157e-10), np.float64(-2.9644580520586977e-10), np.float64(-3.0672797676180796e-10), np.float64(-3.170101483177461e-10), np.float64(-3.2729231987368426e-10), np.float64(-3.3757449142962245e-10), np.float64(-3.4785666298556065e-10), np.float64(-3.581388345414988e-10), np.float64(-3.6842100609743694e-10), np.float64(-3.7870317765337514e-10), np.float64(-3.8898534920931334e-10), np.float64(-3.992675207652515e-10), np.float64(-4.0954969232118963e-10), np.float64(-4.1983186387712783e-10), np.float64(-4.3011403543306603e-10), np.float64(-4.4039620698900417e-10), np.float64(-4.506783785449423e-10), np.float64(-4.609605501008805e-10), np.float64(-4.712427216568187e-10), np.float64(-4.815248932127569e-10), np.float64(-4.918070647686951e-10), np.float64(-5.020892363246333e-10), np.float64(-5.123714078805714e-10), np.float64(-5.226535794365095e-10), np.float64(-5.329357509924477e-10), np.float64(-5.432179225483858e-10)]}
Predicciones para Volatilidad_14 con ventana 14: {0.5: [np.float64(-2.655992905380553e-10), np.float64(-2.758814620939934e-10), np.float64(-2.8616363364993157e-10), np.float64(-2.9644580520586977e-10), np.float64(-3.0672797676180796e-10), np.float64(-3.170101483177461e-10), np.float64(-3.2729231987368426e-10), np.float64(-3.3757449142962245e-10), np.float64(-3.4785666298556065e-10), np.float64(-3.581388345414988e-10), np.float64(-3.6842100609743694e-10), np.float64(-3.7870317765337514e-10), np.float64(-3.8898534920931334e-10), np.float64(-3.992675207652515e-10), np.float64(-4.0954969232118963e-10), np.float64(-4.1983186387712783e-10), np.float64(-4.3011403543306603e-10), np.float64(-4.4039620698900417e-10), np.float64(-4.506783785449423e-10), np.float64(-4.609605501008805e-10), np.float64(-4.712427216568187e-10), np.float64(-4.815248932127569e-10), np.float64(-4.918070647686951e-10), np.float64(-5.020892363246333e-10), np.float64(-5.123714078805714e-10), np.float64(-5.226535794365095e-10), np.float64(-5.329357509924477e-10), np.float64(-5.432179225483858e-10)]}
Predicciones para Volatilidad_14 con ventana 21: {0.5: [np.float64(-2.655992905380553e-10), np.float64(-2.758814620939934e-10), np.float64(-2.8616363364993157e-10), np.float64(-2.9644580520586977e-10), np.float64(-3.0672797676180796e-10), np.float64(-3.170101483177461e-10), np.float64(-3.2729231987368426e-10), np.float64(-3.3757449142962245e-10), np.float64(-3.4785666298556065e-10), np.float64(-3.581388345414988e-10), np.float64(-3.6842100609743694e-10), np.float64(-3.7870317765337514e-10), np.float64(-3.8898534920931334e-10), np.float64(-3.992675207652515e-10), np.float64(-4.0954969232118963e-10), np.float64(-4.1983186387712783e-10), np.float64(-4.3011403543306603e-10), np.float64(-4.4039620698900417e-10), np.float64(-4.506783785449423e-10), np.float64(-4.609605501008805e-10), np.float64(-4.712427216568187e-10), np.float64(-4.815248932127569e-10), np.float64(-4.918070647686951e-10), np.float64(-5.020892363246333e-10), np.float64(-5.123714078805714e-10), np.float64(-5.226535794365095e-10), np.float64(-5.329357509924477e-10), np.float64(-5.432179225483858e-10)]}
Predicciones para Volatilidad_14 con ventana 28: {0.5: [np.float64(-2.655992905380553e-10), np.float64(-2.758814620939934e-10), np.float64(-2.8616363364993157e-10), np.float64(-2.9644580520586977e-10), np.float64(-3.0672797676180796e-10), np.float64(-3.170101483177461e-10), np.float64(-3.2729231987368426e-10), np.float64(-3.3757449142962245e-10), np.float64(-3.4785666298556065e-10), np.float64(-3.581388345414988e-10), np.float64(-3.6842100609743694e-10), np.float64(-3.7870317765337514e-10), np.float64(-3.8898534920931334e-10), np.float64(-3.992675207652515e-10), np.float64(-4.0954969232118963e-10), np.float64(-4.1983186387712783e-10), np.float64(-4.3011403543306603e-10), np.float64(-4.4039620698900417e-10), np.float64(-4.506783785449423e-10), np.float64(-4.609605501008805e-10), np.float64(-4.712427216568187e-10), np.float64(-4.815248932127569e-10), np.float64(-4.918070647686951e-10), np.float64(-5.020892363246333e-10), np.float64(-5.123714078805714e-10), np.float64(-5.226535794365095e-10), np.float64(-5.329357509924477e-10), np.float64(-5.432179225483858e-10)]}
Predicciones para At con ventana 7: {0.5: [np.float64(-4.322978170723535), np.float64(-4.3229781707211155), np.float64(-4.322978170718696), np.float64(-4.322978170716277), np.float64(-4.322978170713857), np.float64(-4.322978170711438), np.float64(-4.3229781707090185), np.float64(-4.322978170706599), np.float64(-4.32297817070418), np.float64(-4.32297817070176), np.float64(-4.322978170699341), np.float64(-4.3229781706969215), np.float64(-4.322978170694502), np.float64(-4.322978170692083), np.float64(-4.322978170689663), np.float64(-4.322978170687244), np.float64(-4.3229781706848245), np.float64(-4.322978170682405), np.float64(-4.322978170679986), np.float64(-4.322978170677566), np.float64(-4.322978170675147), np.float64(-4.3229781706727275), np.float64(-4.322978170670308), np.float64(-4.322978170667889), np.float64(-4.322978170665469), np.float64(-4.32297817066305), np.float64(-4.3229781706606305), np.float64(-4.322978170658211)]}
Predicciones para At con ventana 14: {0.5: [np.float64(-4.322978170723535), np.float64(-4.3229781707211155), np.float64(-4.322978170718696), np.float64(-4.322978170716277), np.float64(-4.322978170713857), np.float64(-4.322978170711438), np.float64(-4.3229781707090185), np.float64(-4.322978170706599), np.float64(-4.32297817070418), np.float64(-4.32297817070176), np.float64(-4.322978170699341), np.float64(-4.3229781706969215), np.float64(-4.322978170694502), np.float64(-4.322978170692083), np.float64(-4.322978170689663), np.float64(-4.322978170687244), np.float64(-4.3229781706848245), np.float64(-4.322978170682405), np.float64(-4.322978170679986), np.float64(-4.322978170677566), np.float64(-4.322978170675147), np.float64(-4.3229781706727275), np.float64(-4.322978170670308), np.float64(-4.322978170667889), np.float64(-4.322978170665469), np.float64(-4.32297817066305), np.float64(-4.3229781706606305), np.float64(-4.322978170658211)]}
Predicciones para At con ventana 21: {0.5: [np.float64(-4.322978170723535), np.float64(-4.3229781707211155), np.float64(-4.322978170718696), np.float64(-4.322978170716277), np.float64(-4.322978170713857), np.float64(-4.322978170711438), np.float64(-4.3229781707090185), np.float64(-4.322978170706599), np.float64(-4.32297817070418), np.float64(-4.32297817070176), np.float64(-4.322978170699341), np.float64(-4.3229781706969215), np.float64(-4.322978170694502), np.float64(-4.322978170692083), np.float64(-4.322978170689663), np.float64(-4.322978170687244), np.float64(-4.3229781706848245), np.float64(-4.322978170682405), np.float64(-4.322978170679986), np.float64(-4.322978170677566), np.float64(-4.322978170675147), np.float64(-4.3229781706727275), np.float64(-4.322978170670308), np.float64(-4.322978170667889), np.float64(-4.322978170665469), np.float64(-4.32297817066305), np.float64(-4.3229781706606305), np.float64(-4.322978170658211)]}
Predicciones para At con ventana 28: {0.5: [np.float64(-4.322978170723535), np.float64(-4.3229781707211155), np.float64(-4.322978170718696), np.float64(-4.322978170716277), np.float64(-4.322978170713857), np.float64(-4.322978170711438), np.float64(-4.3229781707090185), np.float64(-4.322978170706599), np.float64(-4.32297817070418), np.float64(-4.32297817070176), np.float64(-4.322978170699341), np.float64(-4.3229781706969215), np.float64(-4.322978170694502), np.float64(-4.322978170692083), np.float64(-4.322978170689663), np.float64(-4.322978170687244), np.float64(-4.3229781706848245), np.float64(-4.322978170682405), np.float64(-4.322978170679986), np.float64(-4.322978170677566), np.float64(-4.322978170675147), np.float64(-4.3229781706727275), np.float64(-4.322978170670308), np.float64(-4.322978170667889), np.float64(-4.322978170665469), np.float64(-4.32297817066305), np.float64(-4.3229781706606305), np.float64(-4.322978170658211)]}

import numpy as np
import pandas as pd
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Double Exponential Smoothing
def double_exponential_smoothing(series, alpha, beta, n_forecast):
    level = series[0]
    trend = series[1] - series[0]  # Inicializar tendencia
    result = [level + trend]  # Primer pronóstico

    # Suavizado
    for t in range(1, len(series)):
        last_level = level
        level = alpha * series[t] + (1 - alpha) * (last_level + trend)
        trend = beta * (level - last_level) + (1 - beta) * trend

        # Pronóstico
        if t >= len(series) - 1:
            forecast = level + trend
            result.append(forecast)

    # Pronósticos para los próximos n períodos
    forecasts = []
    for i in range(n_forecast):
        forecast = level + (i + 1) * trend
        forecasts.append(forecast)

    return forecasts

# Función para evaluar una variable con D.E.S.
def evaluar_variable_de(variable):
    ventanas = [7, 14, 21, 28]
    alphas = [0.5]
    betas = [0.5]  # También puedes probar diferentes valores para beta
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    for ventana in ventanas:
        for alpha in alphas:
            for beta in betas:
                # Serie de tiempo de entrenamiento sin NaNs
                train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

                # Verificar si hay suficientes datos para el entrenamiento
                if len(train_series) < 1:
                    print(f"Skipping variable '{variable}' for ventana {ventana}, alpha {alpha}, and beta {beta} due to insufficient training data.")
                    continue

                # Obtener las predicciones para el conjunto de validación
                pred_val = double_exponential_smoothing(train_series.values, alpha, beta, test_size)

                # Conjunto de validación real (últimos 28 valores de la serie) sin NaNs
                val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

                # Verificar si hay suficientes datos para la validación
                if len(val_series) < test_size:
                    print(f"Skipping variable '{variable}' for ventana {ventana}, alpha {alpha}, and beta {beta} due to insufficient validation data.")
                    continue

                # Calcular las métricas
                mae = mean_absolute_error(val_series, pred_val)
                mse = mean_squared_error(val_series, pred_val)
                rmse = np.sqrt(mse)
                mape = MAPE(val_series, pred_val)
                r2 = r2_score(val_series, pred_val)

                # Guardar los resultados en una lista
                resultados.append({
                    'Variable': variable,
                    'Ventana': ventana,
                    'Alpha': alpha,
                    'Beta': beta,
                    'MAE': mae,
                    'MSE': mse,
                    'RMSE': rmse,
                    'MAPE': mape,
                    'R2': r2
                })

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales_de = pd.concat([evaluar_variable_de('At'), 
                                    evaluar_variable_de('Price'), 
                                    evaluar_variable_de('Volatilidad_14')], 
                                   ignore_index=True)

# Mostrar la tabla con los resultados totales
print(resultados_totales_de)

          Variable  Ventana  Alpha  Beta           MAE           MSE  \
0               At        7    0.5   0.5  3.007271e-11  1.272532e-21   
1               At       14    0.5   0.5  3.007271e-11  1.272532e-21   
2               At       21    0.5   0.5  3.007271e-11  1.272532e-21   
3               At       28    0.5   0.5  3.007271e-11  1.272532e-21   
4            Price        7    0.5   0.5  5.794263e-12  4.737237e-23   
5            Price       14    0.5   0.5  5.794263e-12  4.737237e-23   
6            Price       21    0.5   0.5  5.794263e-12  4.737237e-23   
7            Price       28    0.5   0.5  5.794263e-12  4.737237e-23   
8   Volatilidad_14        7    0.5   0.5  4.044086e-10  1.704448e-19   
9   Volatilidad_14       14    0.5   0.5  4.044086e-10  1.704448e-19   
10  Volatilidad_14       21    0.5   0.5  4.044086e-10  1.704448e-19   
11  Volatilidad_14       28    0.5   0.5  4.044086e-10  1.704448e-19   

            RMSE          MAPE            R2  
0   3.567257e-11  6.956479e-10  0.000000e+00  
1   3.567257e-11  6.956479e-10  0.000000e+00  
2   3.567257e-11  6.956479e-10  0.000000e+00  
3   3.567257e-11  6.956479e-10  0.000000e+00  
4   6.882759e-12  5.794263e-09 -2.459714e+11  
5   6.882759e-12  5.794263e-09 -2.459714e+11  
6   6.882759e-12  5.794263e-09 -2.459714e+11  
7   6.882759e-12  5.794263e-09 -2.459714e+11  
8   4.128495e-10           inf  0.000000e+00  
9   4.128495e-10           inf  0.000000e+00  
10  4.128495e-10           inf  0.000000e+00  
11  4.128495e-10           inf  0.000000e+00  

Variable	Ventana	Alpha	Beta	MAE	MSE	RMSE	MAPE	R²
At	7	0.5	0.5	3.007271e-11	1.272532e-21	3.567257e-11	6.956479e-10	0.000000e+00
Price	7	0.5	0.5	5.794263e-12	4.737237e-23	6.882759e-12	5.794263e-09	-2.459714e+11
Volatilidad_14	7	0.5	0.5	4.044086e-10	1.704448e-19	4.128495e-10	inf	0.000000e+00

Explicación de la Selección de una Sola Ventana

Se ha seleccionado una única ventana de 7 para presentar los resultados del modelo de doble suavizado exponencial. Esto se hace con el objetivo de simplificar el análisis y facilitar la interpretación de las métricas de rendimiento. Dado que el modelo de suavizado exponencial se basa en la idea de que las observaciones más recientes son más relevantes para hacer predicciones futuras, usar una sola ventana permite concentrarse en cómo el modelo responde a las condiciones más actuales de los datos. Además, al fijar los parámetros Alpha y Beta en 0.5, se mantiene la coherencia en la estimación de las predicciones a través de todas las variables, permitiendo una comparación directa de su rendimiento.

Para la variable “At”, se utilizaron ventanas de 7, 14, 21 y 28, todas con parámetros Alpha y Beta fijados en 0.5. Los valores de MAE (3.007271e-11) y MSE (1.272532e-21) son notablemente bajos, lo que sugiere que las predicciones son muy precisas y están muy cercanas a los valores reales. Esto se refleja también en el RMSE (3.567257e-11), que confirma la robustez de las predicciones en términos de error cuadrático medio. Sin embargo, el MAPE es también bajo (6.956479e-10) y, dado que se aproxima a cero, indica que el error relativo es casi imperceptible. A pesar de estas métricas positivas, el R² se mantiene en 0, lo que sugiere que el modelo no logra explicar la variabilidad de la serie temporal. Esto puede implicar que, aunque las predicciones son precisas, el modelo no está capturando la dinámica subyacente de los datos.

Para la variable “Price”, los resultados son igualmente prometedores, con MAE (5.794263e-12) y MSE (4.737237e-23) que indican un ajuste excepcionalmente preciso. Los valores de RMSE (6.882759e-12) y MAPE (5.794263e-09) son también bajos, pero el R² es -2.459714e+11, lo que sugiere una notable incapacidad del modelo para explicar la variabilidad en esta serie. Este comportamiento puede ser reflejo de que el precio es constante a lo largo del tiempo o de que se presenta un sobreajuste.

Finalmente, para la variable “Volatilidad_14”, se observan resultados con MAE (4.044086e-10) y MSE (1.704448e-19) también bajos, aunque el MAPE es infinito, lo que implica que hay problemas con los valores de referencia en la serie temporal que afectan este cálculo. Esto, combinado con un R² de 0, sugiere que el modelo no está capturando adecuadamente las dinámicas de la volatilidad.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.api as sm
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.stats.stattools import jarque_bera

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Suavizado Exponencial Doble
def double_exponential_smoothing(series, alpha, beta, n_forecast):
    n = len(series)
    result = np.zeros(n + n_forecast)  # Almacena niveles y predicciones
    level = series[0]
    trend = series[1] - series[0]  # Inicializar la tendencia

    result[0] = level

    for t in range(1, n):
        last_level = level
        level = alpha * series[t] + (1 - alpha) * (last_level + trend)
        trend = beta * (level - last_level) + (1 - beta) * trend
        result[t] = level

    # Predicciones futuras
    for i in range(n_forecast):
        result[n + i] = level + (i + 1) * trend

    return result[n:], result[:n]  # Retornar solo las predicciones y los niveles

# Función para evaluar la variable y analizar residuos
def evaluar_variable_con_residuos_de(variable):
    alphas = [0.5]
    betas = [0.5]  # Puedes probar diferentes valores para beta
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    for alpha in alphas:
        for beta in betas:
            # Serie de tiempo de entrenamiento sin NaNs
            train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

            # Verificar que hay suficientes datos para entrenar
            if len(train_series) < 1:
                print(f"Skipping variable '{variable}' due to insufficient training data.")
                continue

            # Obtener las predicciones y niveles para el conjunto de validación
            pred_val, niveles = double_exponential_smoothing(train_series.values, alpha, beta, test_size)

            # Conjunto de validación real (últimos 28 valores de la serie) sin NaNs
            val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

            # Verificar que hay suficientes datos para la validación
            if len(val_series) < test_size:
                print(f"Skipping variable '{variable}' due to insufficient validation data.")
                continue

            # Calcular métricas
            mae = mean_absolute_error(val_series, pred_val)
            mse = mean_squared_error(val_series, pred_val)
            rmse = np.sqrt(mse)
            mape = MAPE(val_series, pred_val)
            r2 = r2_score(val_series, pred_val)

            # Calcular residuos
            residuos = val_series.values - pred_val

            # Verificar la longitud de residuos
            if len(residuos) < 2:  # Necesitamos al menos 2 puntos para hacer análisis
                print(f"Not enough data points in residues for variable '{variable}'. Skipping analysis.")
                continue

            # Pruebas de hipótesis
            ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
            ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan
            jarque_bera_results = jarque_bera(residuos)
            jarque_bera_pvalue = jarque_bera_results[1]

            # Guardar resultados
            resultados.append({
                'Variable': variable,
                'MAPE': mape,
                'MAE': mae,
                'RMSE': rmse,
                'MSE': mse,
                'R2': r2,
                'Ljung-Box (p-value)': ljung_box_pvalue,
                'Jarque-Bera (p-value)': jarque_bera_pvalue
            })

            # Gráficos
            plt.figure(figsize=(15, 5))

            # Serie de residuos
            plt.subplot(1, 3, 1)
            plt.plot(residuos)
            plt.title(f'Serie de residuos: {variable}')
            plt.xlabel('Tiempo')
            plt.ylabel('Residuos')

            # QQPlot
            plt.subplot(1, 3, 2)
            sm.qqplot(residuos, line='s', ax=plt.gca())
            plt.title('QQPlot de residuos')

            # ACF solo si hay suficientes residuos
            if len(residuos) >= 30:
                plt.subplot(1, 3, 3)
                from statsmodels.graphics.tsaplots import plot_acf
                plot_acf(residuos, lags=30, ax=plt.gca())
                plt.title('ACF de residuos')
            else:
                plt.subplot(1, 3, 3)
                plt.text(0.5, 0.5, 'No hay suficientes datos para ACF', 
                         horizontalalignment='center', verticalalignment='center')
                plt.title('ACF de residuos')

            plt.tight_layout()
            plt.show()

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales_de = pd.concat([evaluar_variable_con_residuos_de('At'), 
                                    evaluar_variable_con_residuos_de('Price'), 
                                    evaluar_variable_con_residuos_de('Volatilidad_14')], 
                                   ignore_index=True)

# Mostrar la tabla con los resultados totales
print(resultados_totales_de)

         Variable          MAPE           MAE          RMSE           MSE  \
0              At  6.956479e-10  3.007271e-11  3.567257e-11  1.272532e-21   
1           Price  5.794263e-09  5.794263e-12  6.882759e-12  4.737237e-23   
2  Volatilidad_14           inf  4.044086e-10  4.128495e-10  1.704448e-19   

             R2  Ljung-Box (p-value)  Jarque-Bera (p-value)  
0  0.000000e+00         3.769957e-15                0.42986  
1 -2.459714e+11         3.769963e-15                0.42986  
2  0.000000e+00         3.769957e-15                0.42986  

Variable	MAPE	MAE	RMSE	MSE	R²	Ljung-Box (p-value)	Jarque-Bera (p-value)
At	6.96e-10	3.01e-11	3.57e-11	1.27e-21	0.0	3.77e-15	0.42986
Price	5.79e-09	5.79e-12	6.88e-12	4.74e-23	-2.46e+11	3.77e-15	0.42986
Volatilidad_14	inf	4.04e-10	4.13e-10	1.70e-19	0.0	3.77e-15	0.42986

Los valores de MAPE son extremadamente bajos para las variables At y Price, lo que indica un ajuste muy preciso en términos relativos. Sin embargo, el MAPE para Volatilidad_14 es infinito (inf), lo cual sugiere problemas en el cálculo de porcentaje de error, posiblemente debido a valores cercanos a cero en el denominador. En cuanto al MAE, los valores son pequeños para todas las variables, especialmente para Price, lo que indica que el modelo tiene un error absoluto bajo. Sin embargo, el valor algo elevado en Volatilidad_14 en comparación con At y Price sugiere que el modelo no se ajusta tan bien para la volatilidad.

El RMSE, que penaliza errores más grandes, es bajo en general, pero nuevamente es más alto en Volatilidad_14, lo que confirma que los errores son mayores en esta variable. En cuanto al MSE, este es extremadamente bajo para todas las variables, lo que indica un ajuste en general preciso, aunque presenta el mismo patrón que los errores anteriores, mostrando mayor imprecisión en Volatilidad_14.

Respecto al R², para At y Volatilidad_14 es cero, lo que indica que el modelo no explica la varianza de estas series. Para Price, el valor negativo (-2.46e+11) sugiere un modelo extremadamente ineficaz en su capacidad de predicción para esta serie, con un ajuste incluso peor que el de una línea base horizontal.

Analisis de los graficos

La gráfica de residuos en el tiempo muestra una tendencia descendente clara en los residuos, lo cual indica que el modelo de doble suavizado exponencial no ha capturado adecuadamente el patrón de las series de tiempo, incluyendo las variables de precio, volatilidad y retornos acumulados. En todas estas series, los residuos deberían estar distribuidos alrededor de cero, sin ninguna tendencia visible, para que el modelo pueda considerarse adecuado.

En el gráfico QQ de residuos, se observa una alineación algo cercana a la línea de normalidad, pero en los extremos se presenta una desviación significativa en todas las series. Esto indica que los residuos no siguen perfectamente una distribución normal, lo cual sugiere que el modelo podría no estar capturando toda la variabilidad o podría presentar algún sesgo en la estimación de los valores para las series de tiempo analizadas.

La ausencia de datos en la ACF de residuos probablemente se deba a un número insuficiente de observaciones o a un problema en el cálculo de la ACF. Para que la serie de residuos sea considerada aleatoria, la ACF debería mostrar autocorrelaciones cercanas a cero en todos los rezagos. La falta de una ACF confiable dificulta la evaluación de independencia en los residuos, un aspecto importante para evaluar el ajuste del modelo.

En general, estos resultados sugieren que el modelo de doble suavizado exponencial podría no ser el más adecuado para las series de precio, volatilidad y retornos acumulados del bitcoin, ya que la tendencia en los residuos y la desviación en el QQ Plot indican una posible falta de ajuste. Podría ser conveniente explorar modelos más complejos, como ARIMA o modelos de volatilidad como GARCH, para captar mejor la naturaleza de estas series de tiempo financieras, que suelen presentar patrones de alta volatilidad y autocorrelación que un modelo de suavizado exponencial no alcanza a modelar adecuadamente.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.tsa.holtwinters import Holt
from statsmodels.stats.diagnostic import acorr_ljungbox

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Double Exponential Smoothing
def des_predict(serie, alpha, beta, test_size):
    model = Holt(serie)
    model_fit = model.fit(smoothing_level=alpha, smoothing_slope=beta, optimized=False)
    pred_val = model_fit.forecast(test_size)
    return pred_val, model_fit.resid  # Retornar también los residuos

# Función para evaluar el modelo en el conjunto de prueba
def evaluar_modelo_en_test(variable):
    alphas = [0.5]
    betas = [0.3]  # Puedes ajustar este valor
    train_size = len(df) - 28  # Tamaño del conjunto de entrenamiento
    test_size = 28               # Tamaño del conjunto de prueba

    resultados = []

    for alpha in alphas:
        for beta in betas:
            # Serie de tiempo de entrenamiento sin NaNs
            train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

            # Obtener las predicciones y residuos para el conjunto de prueba
            pred_val, residuos = des_predict(train_series, alpha, beta, test_size)

            # Conjunto de prueba real (últimos 28 valores de la serie) sin NaNs
            val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

            # Calcular métricas
            mae = mean_absolute_error(val_series, pred_val)
            mse = mean_squared_error(val_series, pred_val)
            rmse = np.sqrt(mse)
            mape = MAPE(val_series, pred_val)
            r2 = r2_score(val_series, pred_val)

            # Pruebas de hipótesis
            ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
            ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan

            # Guardar resultados
            resultados.append({
                'Variable': variable,
                'MAPE': mape,
                'MAE': mae,
                'RMSE': rmse,
                'MSE': mse,
                'R2': r2,
                'Ljung-Box (p-value)': ljung_box_pvalue
            })

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales_test = pd.concat([evaluar_modelo_en_test('At'), 
                                      evaluar_modelo_en_test('Price'), 
                                      evaluar_modelo_en_test('Volatilidad_14')], 
                                     ignore_index=True)

# Mostrar la tabla con los resultados totales del conjunto de prueba
print(resultados_totales_test)

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\3045378745.py:15: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\3045378745.py:15: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\3045378745.py:15: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

         Variable  MAPE           MAE          RMSE           MSE  \
0              At   NaN  2.286879e-11  2.428319e-11  5.896734e-22   
1           Price   NaN  4.483255e-12  4.759638e-12  2.265415e-23   
2  Volatilidad_14   NaN  2.715903e-09  3.040632e-09  9.245445e-18   

             R2  Ljung-Box (p-value)  
0  0.000000e+00        1.531841e-226  
1 -1.176271e+11        1.092221e-284  
2  0.000000e+00         0.000000e+00  

Variable	MAPE	MAE	RMSE	MSE	R²	Ljung-Box (p-value)
At	NaN	2.286879e-11	2.428319e-11	5.896734e-22	0.000000e+00	1.531841e-226
Price	NaN	4.483255e-12	4.759638e-12	2.265415e-23	-1.176271e+11	1.092221e-284
Volatilidad_14	NaN	2.715903e-09	3.040632e-09	9.245445e-18	0.000000e+00	0.000000e+00

Los resultados de los residuos de la predicción del modelo de suavizado exponencial doble muestran que el MAPE no está disponible (NaN) para todas las variables, lo cual sugiere que el cálculo del porcentaje de error relativo no es aplicable en este contexto. Esto podría deberse a valores cercanos a cero en el denominador o a una interpretación inadecuada al aplicarlo en el análisis de residuos. En cuanto al MAE, los valores son extremadamente bajos para las series At y Price, lo que indica un error absoluto mínimo en la predicción de estas variables. Sin embargo, la variable Volatilidad_14 presenta un MAE considerablemente mayor, lo cual revela que el modelo de suavizado exponencial doble tiene un rendimiento notablemente inferior al intentar predecir la volatilidad.

El RMSE, al igual que el MAE, es bajo para At y Price, lo que confirma que el modelo produce errores de magnitud pequeña en estas series. No obstante, el RMSE es significativamente más alto en Volatilidad_14, reforzando la idea de que los errores en la predicción de la volatilidad son mayores y que el modelo no logra capturar adecuadamente su comportamiento. Los valores de MSE siguen esta misma tendencia, con valores muy bajos para At y Price, reflejando un ajuste preciso en estas series, mientras que en Volatilidad_14 el MSE es considerablemente más alto, lo cual indica una mayor dispersión de los errores en esta serie.

El R² es cero para At y Volatilidad_14, lo que indica que el modelo no logra explicar ninguna de las variaciones en estas series. Para Price, el R² es negativo (-1.18e+11), lo que sugiere que el modelo es completamente ineficaz en la predicción de esta variable, obteniendo un ajuste peor que el de una línea base horizontal. Además, los valores extremadamente bajos del p-value en el test de Ljung-Box para todas las variables sugieren que los residuos presentan autocorrelación significativa, lo cual indica que no son independientes y que el modelo no ha capturado adecuadamente la estructura temporal de las series.

En conjunto, estos resultados indican que el modelo de suavizado exponencial doble no logra un ajuste adecuado, especialmente en la serie Volatilidad_14. La falta de independencia y el alto error en esta variable sugieren que el modelo subestima o no captura los patrones presentes, particularmente en datos más volátiles.

Double Exponential Smoothing (Usando statsmodels.tsa.holtwinters)

import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.tsa.holtwinters import Holt

# Parámetros
alphas = [0.5]  # Factores de suavización que queremos probar
ventanas = [7, 14, 21, 28]  # Ventanas móviles para cada predicción
variables = ['Price', 'Volatilidad_14', 'At']

# Función para realizar Double Exponential Smoothing usando statsmodels
def double_exponential_smoothing(series, alpha, beta, n_forecast):
    model = Holt(series)
    model_fit = model.fit(smoothing_level=alpha, smoothing_slope=beta, optimized=False)
    
    # Pronósticos para los próximos n períodos
    forecasts = model_fit.forecast(n_forecast)
    
    return forecasts, model_fit.fittedvalues  # Solo devuelve pronósticos y valores ajustados

# Almacenaremos las predicciones
predicciones = {}

# Dividimos el conjunto de validación y entrenamiento
train_size = len(df) - 28
test_size = 28

# Para cada variable y cada ventana
for variable in variables:
    predicciones[variable] = {}
    # Tomamos el conjunto de entrenamiento para esa variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    for ventana in ventanas:
        # Inicializar diccionario para cada ventana
        predicciones[variable][ventana] = {}

        for alpha in alphas:
            # Definir un beta (puedes experimentar con este valor)
            beta = 0.5  

            # Aplicar Double Exponential Smoothing
            val_predictions, y_train_pred = double_exponential_smoothing(train_series.values, alpha, beta, test_size)

            # Guardar las predicciones para esta ventana y alpha
            predicciones[variable][ventana][alpha] = val_predictions

# Mostrar predicciones
for variable in predicciones:
    for ventana in predicciones[variable]:
        print(f"Predicciones para {variable} con ventana {ventana}: {predicciones[variable][ventana]}")

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicciones para Price con ventana 7: [np.float64(72572.82472370268), np.float64(70962.87102441574), np.float64(70180.57742488162), np.float64(70577.4622186235), np.float64(70598.07829052533), np.float64(70529.88802734358), np.float64(69765.60212929739), np.float64(69767.14627821947), np.float64(69673.12267727715), np.float64(69882.0236095976), np.float64(69932.7036312084), np.float64(69487.81940325872), np.float64(69273.84272644838), np.float64(69366.47728585098), np.float64(69477.85895750612), np.float64(69410.60733621173), np.float64(69299.16231247706), np.float64(69044.27359654884), np.float64(69021.2132675692), np.float64(69096.86562066393), np.float64(69073.02190646782), np.float64(69036.86448264269), np.float64(69003.62537522428), np.float64(69014.29828484202), np.float64(69056.69368099143), np.float64(69058.23130254625), np.float64(69063.95393017388), np.float64(68992.55837429232)]
MSE: 4851841337.202127, MAE: 69650.60242424314, R²: -2.5192200533264024e+43

Predicciones para Price con ventana 14: [np.float64(72572.82472370268), np.float64(70962.87102441574), np.float64(70180.57742488162), np.float64(70577.4622186235), np.float64(70598.07829052533), np.float64(70529.88802734358), np.float64(69765.60212929739), np.float64(69767.14627821947), np.float64(69673.12267727715), np.float64(69882.0236095976), np.float64(69932.7036312084), np.float64(69487.81940325872), np.float64(69273.84272644838), np.float64(69366.47728585098), np.float64(69477.85895750612), np.float64(69410.60733621173), np.float64(69299.16231247706), np.float64(69044.27359654884), np.float64(69021.2132675692), np.float64(69096.86562066393), np.float64(69073.02190646782), np.float64(69036.86448264269), np.float64(69003.62537522428), np.float64(69014.29828484202), np.float64(69056.69368099143), np.float64(69058.23130254625), np.float64(69063.95393017388), np.float64(68992.55837429232)]
MSE: 4851841337.202127, MAE: 69650.60242424314, R²: -2.5192200533264024e+43

Predicciones para Price con ventana 21: [np.float64(72572.82472370268), np.float64(70962.87102441574), np.float64(70180.57742488162), np.float64(70577.4622186235), np.float64(70598.07829052533), np.float64(70529.88802734358), np.float64(69765.60212929739), np.float64(69767.14627821947), np.float64(69673.12267727715), np.float64(69882.0236095976), np.float64(69932.7036312084), np.float64(69487.81940325872), np.float64(69273.84272644838), np.float64(69366.47728585098), np.float64(69477.85895750612), np.float64(69410.60733621173), np.float64(69299.16231247706), np.float64(69044.27359654884), np.float64(69021.2132675692), np.float64(69096.86562066393), np.float64(69073.02190646782), np.float64(69036.86448264269), np.float64(69003.62537522428), np.float64(69014.29828484202), np.float64(69056.69368099143), np.float64(69058.23130254625), np.float64(69063.95393017388), np.float64(68992.55837429232)]
MSE: 4851841337.202127, MAE: 69650.60242424314, R²: -2.5192200533264024e+43

Predicciones para Price con ventana 28: [np.float64(72572.82472370268), np.float64(70962.87102441574), np.float64(70180.57742488162), np.float64(70577.4622186235), np.float64(70598.07829052533), np.float64(70529.88802734358), np.float64(69765.60212929739), np.float64(69767.14627821947), np.float64(69673.12267727715), np.float64(69882.0236095976), np.float64(69932.7036312084), np.float64(69487.81940325872), np.float64(69273.84272644838), np.float64(69366.47728585098), np.float64(69477.85895750612), np.float64(69410.60733621173), np.float64(69299.16231247706), np.float64(69044.27359654884), np.float64(69021.2132675692), np.float64(69096.86562066393), np.float64(69073.02190646782), np.float64(69036.86448264269), np.float64(69003.62537522428), np.float64(69014.29828484202), np.float64(69056.69368099143), np.float64(69058.23130254625), np.float64(69063.95393017388), np.float64(68992.55837429232)]
MSE: 4851841337.202127, MAE: 69650.60242424314, R²: -2.5192200533264024e+43

Predicciones para Volatilidad_14 con ventana 7: [np.float64(0.03815179108758726), np.float64(0.037966539414794886), np.float64(0.03838090307659538), np.float64(0.03860503790874569), np.float64(0.03816473637907315), np.float64(0.03815048525747417), np.float64(0.03825393189562654), np.float64(0.03824741347796928), np.float64(0.03822607776655757), np.float64(0.03819934059330779), np.float64(0.038211676472402985), np.float64(0.03833218381350634), np.float64(0.038292914446658), np.float64(0.038273135504198384), np.float64(0.03828315968009288), np.float64(0.03827779266202768), np.float64(0.03827594164285306), np.float64(0.03828551727067711), np.float64(0.038273359529627), np.float64(0.0382742478131256), np.float64(0.03827753568760619), np.float64(0.038276679847233104), np.float64(0.03827636155359623), np.float64(0.038275069130926875), np.float64(0.03827634656130473), np.float64(0.03827620150506399), np.float64(0.03827758595859685), np.float64(0.038275861582451526)]
MSE: 0.0014639953023312916, MAE: 0.038262065268560005, R²: 0.0

Predicciones para Volatilidad_14 con ventana 14: [np.float64(0.03815179108758726), np.float64(0.037966539414794886), np.float64(0.03838090307659538), np.float64(0.03860503790874569), np.float64(0.03816473637907315), np.float64(0.03815048525747417), np.float64(0.03825393189562654), np.float64(0.03824741347796928), np.float64(0.03822607776655757), np.float64(0.03819934059330779), np.float64(0.038211676472402985), np.float64(0.03833218381350634), np.float64(0.038292914446658), np.float64(0.038273135504198384), np.float64(0.03828315968009288), np.float64(0.03827779266202768), np.float64(0.03827594164285306), np.float64(0.03828551727067711), np.float64(0.038273359529627), np.float64(0.0382742478131256), np.float64(0.03827753568760619), np.float64(0.038276679847233104), np.float64(0.03827636155359623), np.float64(0.038275069130926875), np.float64(0.03827634656130473), np.float64(0.03827620150506399), np.float64(0.03827758595859685), np.float64(0.038275861582451526)]
MSE: 0.0014639953023312916, MAE: 0.038262065268560005, R²: 0.0

Predicciones para Volatilidad_14 con ventana 21: [np.float64(0.03815179108758726), np.float64(0.037966539414794886), np.float64(0.03838090307659538), np.float64(0.03860503790874569), np.float64(0.03816473637907315), np.float64(0.03815048525747417), np.float64(0.03825393189562654), np.float64(0.03824741347796928), np.float64(0.03822607776655757), np.float64(0.03819934059330779), np.float64(0.038211676472402985), np.float64(0.03833218381350634), np.float64(0.038292914446658), np.float64(0.038273135504198384), np.float64(0.03828315968009288), np.float64(0.03827779266202768), np.float64(0.03827594164285306), np.float64(0.03828551727067711), np.float64(0.038273359529627), np.float64(0.0382742478131256), np.float64(0.03827753568760619), np.float64(0.038276679847233104), np.float64(0.03827636155359623), np.float64(0.038275069130926875), np.float64(0.03827634656130473), np.float64(0.03827620150506399), np.float64(0.03827758595859685), np.float64(0.038275861582451526)]
MSE: 0.0014639953023312916, MAE: 0.038262065268560005, R²: 0.0

Predicciones para Volatilidad_14 con ventana 28: [np.float64(0.03815179108758726), np.float64(0.037966539414794886), np.float64(0.03838090307659538), np.float64(0.03860503790874569), np.float64(0.03816473637907315), np.float64(0.03815048525747417), np.float64(0.03825393189562654), np.float64(0.03824741347796928), np.float64(0.03822607776655757), np.float64(0.03819934059330779), np.float64(0.038211676472402985), np.float64(0.03833218381350634), np.float64(0.038292914446658), np.float64(0.038273135504198384), np.float64(0.03828315968009288), np.float64(0.03827779266202768), np.float64(0.03827594164285306), np.float64(0.03828551727067711), np.float64(0.038273359529627), np.float64(0.0382742478131256), np.float64(0.03827753568760619), np.float64(0.038276679847233104), np.float64(0.03827636155359623), np.float64(0.038275069130926875), np.float64(0.03827634656130473), np.float64(0.03827620150506399), np.float64(0.03827758595859685), np.float64(0.038275861582451526)]
MSE: 0.0014639953023312916, MAE: 0.038262065268560005, R²: 0.0

Predicciones para At con ventana 7: [np.float64(0.04723382325738659), np.float64(0.02545030900326856), np.float64(0.022848817952236214), np.float64(0.04012766486861653), np.float64(0.038231434124326), np.float64(0.029019413980323257), np.float64(0.04168675610051997), np.float64(0.024846790429878137), np.float64(0.024927636316099233), np.float64(0.027156239795189097), np.float64(0.023799017736755256), np.float64(0.023770129321966958), np.float64(0.02456212363440725), np.float64(0.027211496309687326), np.float64(0.02409643138043594), np.float64(0.026718311201794825), np.float64(0.026161975378552846), np.float64(0.02697435337041726), np.float64(0.026161810650191478), np.float64(0.026910210082171024), np.float64(0.026762678900128543), np.float64(0.026653314414446544), np.float64(0.026600038444436938), np.float64(0.02659566715562109), np.float64(0.026351266415452063), np.float64(0.026351271198588936), np.float64(0.02630954749806174), np.float64(0.026330042410067866)]
MSE: 18.932862807403723, MAE: 4.351187048268252, R²: 0.0

Predicciones para At con ventana 14: [np.float64(0.04723382325738659), np.float64(0.02545030900326856), np.float64(0.022848817952236214), np.float64(0.04012766486861653), np.float64(0.038231434124326), np.float64(0.029019413980323257), np.float64(0.04168675610051997), np.float64(0.024846790429878137), np.float64(0.024927636316099233), np.float64(0.027156239795189097), np.float64(0.023799017736755256), np.float64(0.023770129321966958), np.float64(0.02456212363440725), np.float64(0.027211496309687326), np.float64(0.02409643138043594), np.float64(0.026718311201794825), np.float64(0.026161975378552846), np.float64(0.02697435337041726), np.float64(0.026161810650191478), np.float64(0.026910210082171024), np.float64(0.026762678900128543), np.float64(0.026653314414446544), np.float64(0.026600038444436938), np.float64(0.02659566715562109), np.float64(0.026351266415452063), np.float64(0.026351271198588936), np.float64(0.02630954749806174), np.float64(0.026330042410067866)]
MSE: 18.932862807403723, MAE: 4.351187048268252, R²: 0.0

Predicciones para At con ventana 21: [np.float64(0.04723382325738659), np.float64(0.02545030900326856), np.float64(0.022848817952236214), np.float64(0.04012766486861653), np.float64(0.038231434124326), np.float64(0.029019413980323257), np.float64(0.04168675610051997), np.float64(0.024846790429878137), np.float64(0.024927636316099233), np.float64(0.027156239795189097), np.float64(0.023799017736755256), np.float64(0.023770129321966958), np.float64(0.02456212363440725), np.float64(0.027211496309687326), np.float64(0.02409643138043594), np.float64(0.026718311201794825), np.float64(0.026161975378552846), np.float64(0.02697435337041726), np.float64(0.026161810650191478), np.float64(0.026910210082171024), np.float64(0.026762678900128543), np.float64(0.026653314414446544), np.float64(0.026600038444436938), np.float64(0.02659566715562109), np.float64(0.026351266415452063), np.float64(0.026351271198588936), np.float64(0.02630954749806174), np.float64(0.026330042410067866)]
MSE: 18.932862807403723, MAE: 4.351187048268252, R²: 0.0

Predicciones para At con ventana 28: [np.float64(0.04723382325738659), np.float64(0.02545030900326856), np.float64(0.022848817952236214), np.float64(0.04012766486861653), np.float64(0.038231434124326), np.float64(0.029019413980323257), np.float64(0.04168675610051997), np.float64(0.024846790429878137), np.float64(0.024927636316099233), np.float64(0.027156239795189097), np.float64(0.023799017736755256), np.float64(0.023770129321966958), np.float64(0.02456212363440725), np.float64(0.027211496309687326), np.float64(0.02409643138043594), np.float64(0.026718311201794825), np.float64(0.026161975378552846), np.float64(0.02697435337041726), np.float64(0.026161810650191478), np.float64(0.026910210082171024), np.float64(0.026762678900128543), np.float64(0.026653314414446544), np.float64(0.026600038444436938), np.float64(0.02659566715562109), np.float64(0.026351266415452063), np.float64(0.026351271198588936), np.float64(0.02630954749806174), np.float64(0.026330042410067866)]
MSE: 18.932862807403723, MAE: 4.351187048268252, R²: 0.0

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\statsmodels\base\model.py:607: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

import numpy as np
import pandas as pd
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.tsa.holtwinters import Holt

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Double Exponential Smoothing utilizando statsmodels
def double_exponential_smoothing(series, alpha, beta, n_forecast):
    model = Holt(series)
    model_fit = model.fit(smoothing_level=alpha, smoothing_slope=beta, optimized=False)
    
    # Pronósticos para los próximos n períodos
    forecasts = model_fit.forecast(n_forecast)
    
    return forecasts

# Función para evaluar una variable con D.E.S.
def evaluar_variable_de(variable):
    ventanas = [7, 14, 21, 28]
    alphas = [0.5]
    betas = [0.5]  # También puedes probar diferentes valores para beta
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    for ventana in ventanas:
        for alpha in alphas:
            for beta in betas:
                # Serie de tiempo de entrenamiento sin NaNs
                train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

                # Verificar si hay suficientes datos para el entrenamiento
                if len(train_series) < 1:
                    print(f"Skipping variable '{variable}' for ventana {ventana}, alpha {alpha}, and beta {beta} due to insufficient training data.")
                    continue

                # Obtener las predicciones para el conjunto de validación
                pred_val = double_exponential_smoothing(train_series.values, alpha, beta, test_size)

                # Conjunto de validación real (últimos 28 valores de la serie) sin NaNs
                val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

                # Verificar si hay suficientes datos para la validación
                if len(val_series) < test_size:
                    print(f"Skipping variable '{variable}' for ventana {ventana}, alpha {alpha}, and beta {beta} due to insufficient validation data.")
                    continue

                # Calcular las métricas
                mae = mean_absolute_error(val_series, pred_val)
                mse = mean_squared_error(val_series, pred_val)
                rmse = np.sqrt(mse)
                mape = MAPE(val_series, pred_val)
                r2 = r2_score(val_series, pred_val)

                # Guardar los resultados en una lista
                resultados.append({
                    'Variable': variable,
                    'Ventana': ventana,
                    'Alpha': alpha,
                    'Beta': beta,
                    'MAE': mae,
                    'MSE': mse,
                    'RMSE': rmse,
                    'MAPE': mape,
                    'R2': r2
                })

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales_de = pd.concat([evaluar_variable_de('At'), 
                                    evaluar_variable_de('Price'), 
                                    evaluar_variable_de('Volatilidad_14')], 
                                   ignore_index=True)

# Mostrar la tabla con los resultados totales
print(resultados_totales_de)

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\935398304.py:13: FutureWarning:

the 'smoothing_slope' keyword is deprecated, use 'smoothing_trend' instead.

          Variable  Ventana  Alpha  Beta           MAE           MSE  \
0               At        7    0.5   0.5  3.007271e-11  1.272532e-21   
1               At       14    0.5   0.5  3.007271e-11  1.272532e-21   
2               At       21    0.5   0.5  3.007271e-11  1.272532e-21   
3               At       28    0.5   0.5  3.007271e-11  1.272532e-21   
4            Price        7    0.5   0.5  5.794263e-12  4.737237e-23   
5            Price       14    0.5   0.5  5.794263e-12  4.737237e-23   
6            Price       21    0.5   0.5  5.794263e-12  4.737237e-23   
7            Price       28    0.5   0.5  5.794263e-12  4.737237e-23   
8   Volatilidad_14        7    0.5   0.5  4.044086e-10  1.704448e-19   
9   Volatilidad_14       14    0.5   0.5  4.044086e-10  1.704448e-19   
10  Volatilidad_14       21    0.5   0.5  4.044086e-10  1.704448e-19   
11  Volatilidad_14       28    0.5   0.5  4.044086e-10  1.704448e-19   

            RMSE          MAPE            R2  
0   3.567257e-11  6.956479e-10  0.000000e+00  
1   3.567257e-11  6.956479e-10  0.000000e+00  
2   3.567257e-11  6.956479e-10  0.000000e+00  
3   3.567257e-11  6.956479e-10  0.000000e+00  
4   6.882759e-12  5.794263e-09 -2.459714e+11  
5   6.882759e-12  5.794263e-09 -2.459714e+11  
6   6.882759e-12  5.794263e-09 -2.459714e+11  
7   6.882759e-12  5.794263e-09 -2.459714e+11  
8   4.128495e-10           inf  0.000000e+00  
9   4.128495e-10           inf  0.000000e+00  
10  4.128495e-10           inf  0.000000e+00  
11  4.128495e-10           inf  0.000000e+00  

Variable	Ventana	Alpha	Beta	MAE	MSE	RMSE	MAPE	R2
At	7	0.5	0.5	3.007271e-11	1.272532e-21	3.567257e-11	6.956479e-10	0.000000e+00
Price	7	0.5	0.5	5.794263e-12	4.737237e-23	6.882759e-12	5.794263e-09	-2.459714e+11
Volatilidad_14	7	0.5	0.5	4.044086e-10	1.704448e-19	4.128495e-10	inf	0.000000e+00

En términos de Error Medio Absoluto (MAE), los valores son notablemente bajos para las tres variables. La serie de At presenta un MAE de 3.007271 × 1 0 − 11 3.007271×10 −11 , mientras que el Precio muestra un MAE de 5.794263 × 1 0 − 12 5.794263×10 −12 . Esto indica que el modelo se ajusta mejor a la serie de precio, lo que sugiere un comportamiento más predecible a corto plazo. Por otro lado, la Volatilidad_14 tiene un MAE de 4.044086 × 1 0 − 10 4.044086×10 −10 , lo que indica que esta serie es más difícil de predecir, posiblemente debido a su naturaleza más variable y susceptible a cambios bruscos.

El Error Cuadrático Medio (MSE) también es bajo en general, con un MSE de 1.272532 × 1 0 − 21 1.272532×10 −21 para At, 4.737237 × 1 0 − 23 4.737237×10 −23 para el Precio, y 1.704448 × 1 0 − 19 1.704448×10 −19 para Volatilidad_14. Nuevamente, el precio tiene el MSE más bajo, lo que respalda la idea de que es más fácil de modelar en comparación con las otras series. Esto sugiere que el modelo captura bien las dinámicas del precio, mientras que la volatilidad presenta un comportamiento más errático.

La Raíz del Error Cuadrático Medio (RMSE) sigue la misma tendencia, con valores de 3.567257 × 1 0 − 11 3.567257×10 −11 para At, 6.882759 × 1 0 − 12 6.882759×10 −12 para el Precio, y 4.128495 × 1 0 − 10 4.128495×10 −10 para Volatilidad_14. El RMSE más bajo para el precio refuerza la conclusión de que esta serie es más predecible, mientras que la volatilidad muestra un RMSE más alto, sugiriendo una mayor dispersión en los errores de predicción.

Al analizar el Error Porcentual Absoluto Medio (MAPE), se encuentran resultados interesantes. El MAPE para At es prácticamente cero, lo que indica que el modelo ha realizado predicciones muy cercanas a los valores reales. Sin embargo, para Precio, el MAPE es más alto, lo que señala una menor precisión en términos porcentuales. La situación es más crítica para Volatilidad_14, donde el MAPE se presenta como infinito (inf), indicando problemas en el cálculo de errores porcentuales sobre valores cercanos a cero.

Por último, el coeficiente de determinación R² muestra un panorama preocupante. Tanto para At como para Volatilidad_14, el R² es cero, lo que implica que el modelo no explica la variabilidad de estas series. Esto es un indicativo claro de que el suavizado exponencial doble puede no ser el enfoque adecuado para estas variables. Para el Precio, el R² negativo de − 2.459714 × 1 0 11 −2.459714×10 11 es alarmante, sugiriendo que el modelo se ajusta muy mal a esta serie.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.holtwinters import ExponentialSmoothing
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.graphics.gofplots import qqplot
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.graphics.tsaplots import plot_acf
from scipy.stats import jarque_bera

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar el ajuste y la evaluación del modelo Double Exponential Smoothing
def evaluar_modelo_residuos(variable):
    ventanas = [7, 14, 21, 28]
    alphas = [0.5]
    betas = [0.5]  # También puedes probar diferentes valores para beta
    train_size = len(df) - 28
    test_size = 28

    resultados = []

    for ventana in ventanas:
        for alpha in alphas:
            for beta in betas:
                # Serie de tiempo de entrenamiento sin NaNs
                train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

                # Verificar si hay suficientes datos para el entrenamiento
                if len(train_series) < 2:
                    print(f"Skipping variable '{variable}' for ventana {ventana}, alpha {alpha}, and beta {beta} due to insufficient training data.")
                    continue

                # Ajustar el modelo Double Exponential Smoothing
                model = ExponentialSmoothing(train_series, trend="add", damped_trend=False).fit(smoothing_level=alpha, smoothing_trend=beta)

                # Predicciones en el conjunto de entrenamiento
                fitted_values = model.fittedvalues

                # Calcular los residuos (observados - predichos)
                residuos = train_series.values - fitted_values

                # Calcular métricas de error
                mae = mean_absolute_error(train_series, fitted_values)
                mse = mean_squared_error(train_series, fitted_values)
                rmse = np.sqrt(mse)
                mape = MAPE(train_series, fitted_values)
                r2 = r2_score(train_series, fitted_values)

                # Prueba de independencia (Ljung-Box)
                ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
                ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan

                # Prueba de normalidad (Jarque-Bera) desde scipy
                jarque_bera_stat, jarque_bera_pvalue = jarque_bera(residuos)

                # Guardar resultados
                resultados.append({
                    'Variable': variable,
                    'Ventana': ventana,
                    'Alpha': alpha,
                    'Beta': beta,
                    'MAPE': mape,
                    'MAE': mae,
                    'MSE': mse,
                    'RMSE': rmse,
                    'R2': r2,
                    'LJung-Box (p-value)': ljung_box_pvalue,
                    'Jarque-Bera (p-value)': jarque_bera_pvalue
                })

                # Visualización
                plt.figure(figsize=(12, 8))

                # Serie de residuos
                plt.subplot(3, 1, 1)
                plt.plot(residuos, label="Residuos")
                plt.axhline(0, color='red', linestyle='--', lw=2)
                plt.title(f'Residuals for {variable} (Window {ventana}, Alpha {alpha}, Beta {beta})')
                plt.legend()

                # QQPlot para residuos
                plt.subplot(3, 1, 2)
                qqplot(residuos, line='s', ax=plt.gca())
                plt.title('QQPlot de Residuos')

                # ACF de residuos, asegurando que haya suficientes datos
                if len(residuos) > 1:
                    plt.subplot(3, 1, 3)
                    plot_acf(residuos, ax=plt.gca())
                    plt.title('ACF de Residuos')
                else:
                    print("No hay suficientes residuos para calcular el ACF.")

                plt.tight_layout()
                plt.show()

    return pd.DataFrame(resultados)

# Evaluar los residuos para las tres variables de interés
resultados_residuos_at = evaluar_modelo_residuos('At')
resultados_residuos_price = evaluar_modelo_residuos('Price')
resultados_residuos_volatilidad = evaluar_modelo_residuos('Volatilidad_14')

# Combinar los resultados de las tres variables en una sola tabla
resultados_totales_residuos = pd.concat([resultados_residuos_at, 
                                         resultados_residuos_price, 
                                         resultados_residuos_volatilidad], 
                                        ignore_index=True)

# Mostrar la tabla con los resultados combinados
print(resultados_totales_residuos)

          Variable  Ventana  Alpha  Beta       MAPE         MAE  \
0               At        7    0.5   0.5  11.766277    0.039697   
1               At       14    0.5   0.5  11.766277    0.039697   
2               At       21    0.5   0.5  11.766277    0.039697   
3               At       28    0.5   0.5  11.766277    0.039697   
4            Price        7    0.5   0.5   4.040196  344.475492   
5            Price       14    0.5   0.5   4.040196  344.475492   
6            Price       21    0.5   0.5   4.040196  344.475492   
7            Price       28    0.5   0.5   4.040196  344.475492   
8   Volatilidad_14        7    0.5   0.5        inf    0.004671   
9   Volatilidad_14       14    0.5   0.5        inf    0.004671   
10  Volatilidad_14       21    0.5   0.5        inf    0.004671   
11  Volatilidad_14       28    0.5   0.5        inf    0.004671   

              MSE        RMSE        R2  LJung-Box (p-value)  \
0        0.005099    0.071409  0.996973        1.106629e-246   
1        0.005099    0.071409  0.996973        1.106629e-246   
2        0.005099    0.071409  0.996973        1.106629e-246   
3        0.005099    0.071409  0.996973        1.106629e-246   
4   641546.226847  800.965809  0.997467        5.033189e-284   
5   641546.226847  800.965809  0.997467        5.033189e-284   
6   641546.226847  800.965809  0.997467        5.033189e-284   
7   641546.226847  800.965809  0.997467        5.033189e-284   
8        0.000109    0.010464  0.942980        2.625957e-284   
9        0.000109    0.010464  0.942980        2.625957e-284   
10       0.000109    0.010464  0.942980        2.625957e-284   
11       0.000109    0.010464  0.942980        2.625957e-284   

    Jarque-Bera (p-value)  
0                     0.0  
1                     0.0  
2                     0.0  
3                     0.0  
4                     0.0  
5                     0.0  
6                     0.0  
7                     0.0  
8                     0.0  
9                     0.0  
10                    0.0  
11                    0.0  

Variable	Ventana	Alpha	Beta	MAPE	MAE	MSE	RMSE	R2	LJung-Box (p-value)
At	7	0.5	0.5	11.766277	0.039697	0.005099	0.071409	0.996973	1.106629e-246
Price	7	0.5	0.5	4.040196	344.475492	641546.226847	800.965809	0.997467	5.033189e-284
Volatilidad_14	7	0.5	0.5	inf	0.004671	0.000109	0

Al analizar los resultados obtenidos para los residuos del entrenamiento del modelo de suavizado exponencial doble utilizando la librería Statsmodels, se pueden extraer conclusiones importantes. En cuanto a las métricas de error, para la variable de retornos acumulados (At), el MAPE es de 11.77 y el MAE de 0.0397, lo que indica un nivel de error razonable en las predicciones. La MSE de 0.0051 y el RMSE de 0.0714 refuerzan que el modelo se ajusta bien, ya que estos valores son relativamente bajos.

Por otro lado, en el caso de la variable de precio, el MAPE es notablemente más bajo, alcanzando 4.04, pero el MAE llega a 344.48, sugiriendo que, aunque las predicciones son más precisas en términos porcentuales, el valor absoluto de los errores es muy alto. Esto se ve reflejado en una MSE de 641546.23, lo que indica una variabilidad significativa en los errores, y un RMSE de 800.97, que es bastante alto. Este comportamiento sugiere que las predicciones del modelo son inestables para la variable de precio.

Respecto a la volatilidad, los resultados muestran un MAPE de infinito, lo que indica que hay problemas en la predicción de esta variable. Sin embargo, el MAE es bajo, alcanzando solo 0.0047, lo que sugiere que el modelo no está capturando adecuadamente la dinámica de la volatilidad. A pesar de esto, el MSE es muy bajo, indicando que los errores absolutos son pequeños, pero la naturaleza infinita del MAPE sugiere que el modelo tiene dificultades para ajustarse a esta variable.

En cuanto a la medida de R², para los retornos acumulados (At) se obtiene un valor de 0.997, lo que indica que el modelo explica casi el 99.7% de la variabilidad en los datos. Este es un resultado excelente y sugiere que el modelo de suavizado exponencial doble es muy efectivo para esta serie temporal. Por su parte, el R² para el precio es de 0.997467, que también es alto, aunque el MAE sugiere que los errores son considerablemente altos en términos absolutos. Esto indica que, a pesar de que el modelo se ajusta bien a la serie, no está logrando una buena predicción en todas las instancias. En el caso de la volatilidad, el R² es de 0.942980, lo que es aceptable, pero indica que el modelo no captura tan bien la dinámica de esta variable en comparación con las otras.

Finalmente, al evaluar la autocorrelación en los residuos utilizando el test de Ljung-Box, se observan valores p extremadamente bajos (del orden de 1.106629e-246 para los retornos acumulados y 5.033189e-284 para el precio), lo que sugiere que hay autocorrelación en los residuos, indicando que el modelo podría no haber capturado completamente la dinámica de las series temporales. Esto es una señal de que, aunque el modelo se ajusta bien en términos de error, puede haber patrones en los residuos que no se están considerando adecuadamente. Para la volatilidad, el p-value también es bajo (2.625957e-284), lo que refuerza la idea de que hay correlación en los residuos y que el modelo no está capturando completamente las características de esta variable.

Analisis de los graficos:

Análisis de Residuos

Gráfico de Residuos en el Tiempo:

En esta gráfica, los residuos se distribuyen mayormente alrededor de la línea de cero (marcada en rojo), indicando una mejora significativa en comparación con el primer gráfico presentado. Aunque aún se observan algunos picos significativos, la mayoría de los residuos están más controlados, sugiriendo un ajuste más cercano al comportamiento de la serie temporal de retornos acumulados del bitcoin. Este patrón también se refleja en los residuos de las variables de precio y volatilidad, donde se nota un comportamiento similar, lo que sugiere que el modelo de suavizado exponencial ha capturado adecuadamente las dinámicas subyacentes de las tres series. Sin embargo, los picos presentes indican la existencia de eventos atípicos o volatilidad, algo común en series financieras. Estos picos podrían estar asociados a eventos de mercado, lo que plantea la necesidad de considerar un modelo que gestione mejor la heterocedasticidad, como un GARCH.

QQ Plot de Residuos:

En el QQ Plot, los puntos se alinean mejor con la línea roja (distribución normal teórica) en el rango intermedio de valores, lo que sugiere que los residuos son aproximadamente normales en gran parte de los datos. Sin embargo, se observan desviaciones notables en los extremos (colas), lo que implica que la distribución de los residuos presenta colas más gruesas que la normal. Esta característica de colas gruesas es típica en series de tiempo financieras, y se ha observado también en los residuos de las variables de precio y volatilidad. Esto podría ser beneficioso para explorar modelos que tengan en cuenta este comportamiento, como modelos con distribuciones t o variantes robustas de suavizado exponencial.

ACF de Residuos:

La ACF de los residuos muestra pocos picos significativos en los primeros rezagos, pero en general, los residuos están relativamente descorrelacionados. Esto es una buena señal, ya que indica que el modelo ha capturado la mayoría de la autocorrelación presente en la serie original. Este mismo patrón se observa en las series de precio y volatilidad, donde los residuos también muestran un comportamiento descorrelacionado. Aunque la autocorrelación no es completamente nula, los valores bajos sugieren que los residuos son aproximadamente independientes, lo cual es deseable en un buen ajuste de modelo.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.tsa.holtwinters import Holt
from statsmodels.stats.diagnostic import acorr_ljungbox

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar predicciones con Double Exponential Smoothing
def des_predict(serie, alpha, beta, test_size):
    model = Holt(serie)
    model_fit = model.fit(smoothing_level=alpha, smoothing_trend=beta, optimized=False)  # Cambiado a smoothing_trend
    pred_val = model_fit.forecast(test_size)
    return pred_val, model_fit.resid  # Retornar también los residuos

# Función para evaluar el modelo en el conjunto de prueba
def evaluar_modelo_en_test(variable):
    alphas = [0.5]  # Puedes ajustar el valor de alpha
    betas = [0.3]   # Puedes ajustar el valor de beta
    train_size = len(df) - 28  # Tamaño del conjunto de entrenamiento
    test_size = 28  # Tamaño del conjunto de prueba

    resultados = []

    for alpha in alphas:
        for beta in betas:
            # Serie de tiempo de entrenamiento sin NaNs
            train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

            # Verificar que haya suficientes datos para el entrenamiento
            if len(train_series) < 2:
                print(f"Skipping variable '{variable}' due to insufficient training data.")
                continue

            # Obtener las predicciones y residuos para el conjunto de prueba
            pred_val, residuos = des_predict(train_series, alpha, beta, test_size)

            # Conjunto de prueba real (últimos 28 valores de la serie) sin NaNs
            val_series = df[variable].iloc[-test_size:].dropna().reset_index(drop=True)

            # Asegurarse de que el tamaño de las predicciones y la serie de prueba coincidan
            if len(pred_val) != len(val_series):
                print(f"Skipping variable '{variable}' due to mismatch in prediction and validation set lengths.")
                continue

            # Calcular métricas
            mae = mean_absolute_error(val_series, pred_val)
            mse = mean_squared_error(val_series, pred_val)
            rmse = np.sqrt(mse)
            mape = MAPE(val_series, pred_val)
            r2 = r2_score(val_series, pred_val)

            # Pruebas de hipótesis
            ljung_box_results = acorr_ljungbox(residuos, lags=[10], return_df=True)
            ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0] if not ljung_box_results.empty else np.nan

            # Guardar resultados
            resultados.append({
                'Variable': variable,
                'MAPE': mape,
                'MAE': mae,
                'RMSE': rmse,
                'MSE': mse,
                'R2': r2,
                'Ljung-Box (p-value)': ljung_box_pvalue
            })

    return pd.DataFrame(resultados)

# Evaluar cada variable y combinar los resultados
resultados_totales_test = pd.concat([evaluar_modelo_en_test('At'), 
                                      evaluar_modelo_en_test('Price'), 
                                      evaluar_modelo_en_test('Volatilidad_14')], 
                                     ignore_index=True)

# Mostrar la tabla con los resultados totales del conjunto de prueba
print(resultados_totales_test)

         Variable  MAPE           MAE          RMSE           MSE  \
0              At   NaN  2.286879e-11  2.428319e-11  5.896734e-22   
1           Price   NaN  4.483255e-12  4.759638e-12  2.265415e-23   
2  Volatilidad_14   NaN  2.715903e-09  3.040632e-09  9.245445e-18   

             R2  Ljung-Box (p-value)  
0  0.000000e+00        1.531841e-226  
1 -1.176271e+11        1.092221e-284  
2  0.000000e+00         0.000000e+00  

Variable	MAPE	MAE	RMSE	MSE	R2	Ljung-Box (p-value)
At	NaN	2.286879e-11	2.428319e-11	5.896734e-22	0.000000e+00	1.531841e-226
Price	NaN	4.483255e-12	4.759638e-12	2.265415e-23	-1.176271e+11	1.092221e-284
Volatilidad_14	NaN	2.715903e-09	3.040632e-09	9.245445e-18	0.000000e+00	0.000000e+00

Al examinar los resultados de los residuos de la predicción del modelo de suavizado exponencial doble, se observa un panorama interesante sobre el desempeño del modelo en las diferentes variables analizadas.

Para la variable de retornos acumulados (At), el MAE es de 2.286879 × 1 0 − 11 2.286879×10 −11 y el RMSE es de 2.428319 × 1 0 − 11 2.428319×10 −11 , lo que indica un nivel de error muy bajo en las predicciones. Esto sugiere que el modelo está realizando pronósticos precisos, con una MSE de 5.896734 × 1 0 − 22 5.896734×10 −22 que refuerza la calidad del ajuste. Sin embargo, el R² es de 0, lo que indica que el modelo no explica ninguna variabilidad en los datos de esta variable. Esto es preocupante, ya que sugiere que, a pesar de los errores absolutos bajos, el modelo no está capturando adecuadamente la dinámica de los retornos acumulados.

En el caso de la variable de precio, el MAE se sitúa en 4.483255 × 1 0 − 12 4.483255×10 −12 , lo que también refleja un error bajo en términos absolutos, mientras que el RMSE es de 4.759638 × 1 0 − 12 4.759638×10 −12 y la MSE de 2.265415 × 1 0 − 23 2.265415×10 −23 , lo que muestra un desempeño similar al de la variable de retornos acumulados. Sin embargo, el R² de -1.176271e+11 es notablemente negativo, lo que implica que el modelo no solo falla en explicar la variabilidad de la serie, sino que también sugiere un ajuste muy pobre, posiblemente indicando que el modelo está inadecuado para los datos de precios.

Finalmente, en lo que respecta a la volatilidad, el MAE de 2.715903 × 1 0 − 09 2.715903×10 −09 y el RMSE de 3.040632 × 1 0 − 09 3.040632×10 −09 muestran errores en términos absolutos más altos que en las otras variables, pero aún así son bastante bajos. La MSE es de 9.245445 × 1 0 − 18 9.245445×10 −18 , lo que también sugiere un buen ajuste en términos de error absoluto. No obstante, el R² es nuevamente cero, lo que indica que el modelo no captura la dinámica de la volatilidad en absoluto.

Al observar los valores del test de Ljung-Box, se evidencian p-values extremadamente bajos para todas las variables, indicando que hay autocorrelación significativa en los residuos, lo que sugiere que el modelo no ha capturado completamente la dinámica temporal de las series. Para los retornos acumulados, el p-value es de 1.531841 × 1 0 − 226 1.531841×10 −226 ; para el precio, es de 1.092221 × 1 0 − 284 1.092221×10 −284 ; y para la volatilidad, es de 0.000000 0.000000. Esto refuerza la idea de que el modelo de suavizado exponencial doble podría no ser el más adecuado para estas series, especialmente si se consideran las características típicas de las series temporales financieras.

Modelo Arima (Usando Rolling)

import pandas as pd
import numpy as np
import warnings  # Para suprimir advertencias
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.tsa.arima.model import ARIMA

# Suprimir advertencias de convergencia
warnings.filterwarnings("ignore", message=".*Maximum Likelihood optimization failed to converge.*")
warnings.filterwarnings("ignore", message=".*Non-stationary starting autoregressive parameters found.*")
warnings.filterwarnings("ignore", message=".*Non-invertible starting MA parameters found.*")

# Función para calcular MAPE
def mean_absolute_percentage_error(y_true, y_pred):
    y_true, y_pred = np.array(y_true), np.array(y_pred)
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para realizar ARIMA con rolling window
def arima_rolling(series, p, d, q, window_size, n_forecast):
    history = list(series[:window_size])  # Inicialmente tomar los primeros 'window_size' valores como historia
    predictions = []
    
    for t in range(n_forecast):
        # Ajustar ARIMA en la ventana
        model = ARIMA(history, order=(p, d, q))
        model_fit = model.fit()
        
        # Predecir el siguiente valor
        forecast = model_fit.forecast(steps=1)[0]
        predictions.append(forecast)
        
        # Actualizar la historia con el nuevo valor
        history.append(forecast)
        history.pop(0)  # Limitar el tamaño de la historia al tamaño de la ventana
        
    return predictions

# Parámetros
ventanas = [7, 14, 21, 28]  # Ventanas de predicción
variables = ['Price', 'Volatilidad_14', 'At']

# Almacenaremos las predicciones y métricas
predicciones = {}

# Dividimos el conjunto de validación y entrenamiento
train_size = len(df) - 28
test_size = 28

# Para cada variable y cada ventana
for variable in variables:
    predicciones[variable] = {}
    # Tomamos el conjunto de entrenamiento para esa variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    for ventana in ventanas:
        # Inicializar diccionario para cada ventana
        predicciones[variable][ventana] = {}

        # Definir parámetros ARIMA
        p, d, q = 2, 2, 5  # Puedes ajustar estos parámetros según necesidad

        # Aplicar ARIMA con rolling window de tamaño 14
        val_predictions = arima_rolling(train_series.values, p, d, q, window_size=14, n_forecast=test_size)

        # Guardar las predicciones para esta ventana
        predicciones[variable][ventana]['predictions'] = val_predictions

        # Evaluar en el conjunto de validación
        y_true = df[variable].iloc[train_size:].values  # Valores reales de validación

        # Métricas de error
        mse = mean_squared_error(y_true, val_predictions)
        mae = mean_absolute_error(y_true, val_predictions)
        rmse = np.sqrt(mse)  # RMSE es la raíz cuadrada del MSE
        r2 = r2_score(y_true, val_predictions)
        mape = mean_absolute_percentage_error(y_true, val_predictions)

        # Guardar las métricas en el diccionario
        predicciones[variable][ventana]['mse'] = mse
        predicciones[variable][ventana]['mae'] = mae
        predicciones[variable][ventana]['rmse'] = rmse
        predicciones[variable][ventana]['r2'] = r2
        predicciones[variable][ventana]['mape'] = mape

        # Mostrar los resultados del modelo actual
        print(f"\nResultados para {variable} con ventana {ventana}:")
        print(f"Modelo ARIMA(p={p}, d={d}, q={q})")
        print(f"Predicciones: {predicciones[variable][ventana]['predictions']}")
        print(f"MSE: {predicciones[variable][ventana]['mse']}")
        print(f"MAE: {predicciones[variable][ventana]['mae']}")
        print(f"RMSE: {predicciones[variable][ventana]['rmse']}")
        print(f"R²: {predicciones[variable][ventana]['r2']}")
        print(f"MAPE: {predicciones[variable][ventana]['mape']}%")

Resultados para Price con ventana 7:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(71936.04264106308), np.float64(71131.95142390691), np.float64(70454.81408034434), np.float64(70036.46667081754), np.float64(69616.01516889925), np.float64(69305.9955749856), np.float64(68990.24825091186), np.float64(68694.48418692414), np.float64(68419.1339571371), np.float64(68148.09069806633), np.float64(67875.27679369877), np.float64(67607.58745212312), np.float64(67322.37578719298), np.float64(67014.49838813824), np.float64(66703.50403959658), np.float64(66383.75278129114), np.float64(66079.04250538522), np.float64(65766.63847679693), np.float64(65463.025575629006), np.float64(65159.16062149808), np.float64(64854.31681890181), np.float64(64549.72161091137), np.float64(64241.546763007456), np.float64(63938.06408990121), np.float64(63632.13774770242), np.float64(63325.387826914106), np.float64(63019.863542541825), np.float64(62711.72513219054)]
MSE: 4478145596.178828
MAE: 66870.64530737417
RMSE: 66918.94796078932
R²: -2.3251861311100903e+43
MAPE: 66870645.307374164%

Resultados para Price con ventana 14:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(71936.04264106308), np.float64(71131.95142390691), np.float64(70454.81408034434), np.float64(70036.46667081754), np.float64(69616.01516889925), np.float64(69305.9955749856), np.float64(68990.24825091186), np.float64(68694.48418692414), np.float64(68419.1339571371), np.float64(68148.09069806633), np.float64(67875.27679369877), np.float64(67607.58745212312), np.float64(67322.37578719298), np.float64(67014.49838813824), np.float64(66703.50403959658), np.float64(66383.75278129114), np.float64(66079.04250538522), np.float64(65766.63847679693), np.float64(65463.025575629006), np.float64(65159.16062149808), np.float64(64854.31681890181), np.float64(64549.72161091137), np.float64(64241.546763007456), np.float64(63938.06408990121), np.float64(63632.13774770242), np.float64(63325.387826914106), np.float64(63019.863542541825), np.float64(62711.72513219054)]
MSE: 4478145596.178828
MAE: 66870.64530737417
RMSE: 66918.94796078932
R²: -2.3251861311100903e+43
MAPE: 66870645.307374164%

Resultados para Price con ventana 21:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(71936.04264106308), np.float64(71131.95142390691), np.float64(70454.81408034434), np.float64(70036.46667081754), np.float64(69616.01516889925), np.float64(69305.9955749856), np.float64(68990.24825091186), np.float64(68694.48418692414), np.float64(68419.1339571371), np.float64(68148.09069806633), np.float64(67875.27679369877), np.float64(67607.58745212312), np.float64(67322.37578719298), np.float64(67014.49838813824), np.float64(66703.50403959658), np.float64(66383.75278129114), np.float64(66079.04250538522), np.float64(65766.63847679693), np.float64(65463.025575629006), np.float64(65159.16062149808), np.float64(64854.31681890181), np.float64(64549.72161091137), np.float64(64241.546763007456), np.float64(63938.06408990121), np.float64(63632.13774770242), np.float64(63325.387826914106), np.float64(63019.863542541825), np.float64(62711.72513219054)]
MSE: 4478145596.178828
MAE: 66870.64530737417
RMSE: 66918.94796078932
R²: -2.3251861311100903e+43
MAPE: 66870645.307374164%

Resultados para Price con ventana 28:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(71936.04264106308), np.float64(71131.95142390691), np.float64(70454.81408034434), np.float64(70036.46667081754), np.float64(69616.01516889925), np.float64(69305.9955749856), np.float64(68990.24825091186), np.float64(68694.48418692414), np.float64(68419.1339571371), np.float64(68148.09069806633), np.float64(67875.27679369877), np.float64(67607.58745212312), np.float64(67322.37578719298), np.float64(67014.49838813824), np.float64(66703.50403959658), np.float64(66383.75278129114), np.float64(66079.04250538522), np.float64(65766.63847679693), np.float64(65463.025575629006), np.float64(65159.16062149808), np.float64(64854.31681890181), np.float64(64549.72161091137), np.float64(64241.546763007456), np.float64(63938.06408990121), np.float64(63632.13774770242), np.float64(63325.387826914106), np.float64(63019.863542541825), np.float64(62711.72513219054)]
MSE: 4478145596.178828
MAE: 66870.64530737417
RMSE: 66918.94796078932
R²: -2.3251861311100903e+43
MAPE: 66870645.307374164%

Resultados para Volatilidad_14 con ventana 7:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.0336689953651134), np.float64(0.0326459420599343), np.float64(0.033163609179256946), np.float64(0.03339935919549996), np.float64(0.033256724551139975), np.float64(0.03213356256450612), np.float64(0.0314998980599837), np.float64(0.031026578229738647), np.float64(0.03041871802498638), np.float64(0.02983864059031928), np.float64(0.029258568244626377), np.float64(0.028678497356694213), np.float64(0.028098426653382115), np.float64(0.027518355874431695), np.float64(0.026938285096005998), np.float64(0.026358214317580734), np.float64(0.025778143539155467), np.float64(0.025198072760730206), np.float64(0.024618001982304946), np.float64(0.024037931203879686), np.float64(0.023457860425454426), np.float64(0.022877789645536342), np.float64(0.02229771886561826), np.float64(0.021717648085700175), np.float64(0.021137577305782092), np.float64(0.02055750652586401), np.float64(0.019977435745945925), np.float64(0.01939736496602784)]
MSE: 0.0007550048702026055
MAE: 0.027105550943399972
RMSE: 0.027477351950335488
R²: 0.0
MAPE: inf%

Resultados para Volatilidad_14 con ventana 14:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.0336689953651134), np.float64(0.0326459420599343), np.float64(0.033163609179256946), np.float64(0.03339935919549996), np.float64(0.033256724551139975), np.float64(0.03213356256450612), np.float64(0.0314998980599837), np.float64(0.031026578229738647), np.float64(0.03041871802498638), np.float64(0.02983864059031928), np.float64(0.029258568244626377), np.float64(0.028678497356694213), np.float64(0.028098426653382115), np.float64(0.027518355874431695), np.float64(0.026938285096005998), np.float64(0.026358214317580734), np.float64(0.025778143539155467), np.float64(0.025198072760730206), np.float64(0.024618001982304946), np.float64(0.024037931203879686), np.float64(0.023457860425454426), np.float64(0.022877789645536342), np.float64(0.02229771886561826), np.float64(0.021717648085700175), np.float64(0.021137577305782092), np.float64(0.02055750652586401), np.float64(0.019977435745945925), np.float64(0.01939736496602784)]
MSE: 0.0007550048702026055
MAE: 0.027105550943399972
RMSE: 0.027477351950335488
R²: 0.0
MAPE: inf%

Resultados para Volatilidad_14 con ventana 21:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.0336689953651134), np.float64(0.0326459420599343), np.float64(0.033163609179256946), np.float64(0.03339935919549996), np.float64(0.033256724551139975), np.float64(0.03213356256450612), np.float64(0.0314998980599837), np.float64(0.031026578229738647), np.float64(0.03041871802498638), np.float64(0.02983864059031928), np.float64(0.029258568244626377), np.float64(0.028678497356694213), np.float64(0.028098426653382115), np.float64(0.027518355874431695), np.float64(0.026938285096005998), np.float64(0.026358214317580734), np.float64(0.025778143539155467), np.float64(0.025198072760730206), np.float64(0.024618001982304946), np.float64(0.024037931203879686), np.float64(0.023457860425454426), np.float64(0.022877789645536342), np.float64(0.02229771886561826), np.float64(0.021717648085700175), np.float64(0.021137577305782092), np.float64(0.02055750652586401), np.float64(0.019977435745945925), np.float64(0.01939736496602784)]
MSE: 0.0007550048702026055
MAE: 0.027105550943399972
RMSE: 0.027477351950335488
R²: 0.0
MAPE: inf%

Resultados para Volatilidad_14 con ventana 28:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.0336689953651134), np.float64(0.0326459420599343), np.float64(0.033163609179256946), np.float64(0.03339935919549996), np.float64(0.033256724551139975), np.float64(0.03213356256450612), np.float64(0.0314998980599837), np.float64(0.031026578229738647), np.float64(0.03041871802498638), np.float64(0.02983864059031928), np.float64(0.029258568244626377), np.float64(0.028678497356694213), np.float64(0.028098426653382115), np.float64(0.027518355874431695), np.float64(0.026938285096005998), np.float64(0.026358214317580734), np.float64(0.025778143539155467), np.float64(0.025198072760730206), np.float64(0.024618001982304946), np.float64(0.024037931203879686), np.float64(0.023457860425454426), np.float64(0.022877789645536342), np.float64(0.02229771886561826), np.float64(0.021717648085700175), np.float64(0.021137577305782092), np.float64(0.02055750652586401), np.float64(0.019977435745945925), np.float64(0.01939736496602784)]
MSE: 0.0007550048702026055
MAE: 0.027105550943399972
RMSE: 0.027477351950335488
R²: 0.0
MAPE: inf%

Resultados para At con ventana 7:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.02850165694401747), np.float64(0.031828707456130555), np.float64(0.013315700225826795), np.float64(0.04618203804615304), np.float64(0.06566488278172859), np.float64(0.07506609787221218), np.float64(0.08185428916815615), np.float64(0.07644556723390318), np.float64(0.06533253101918013), np.float64(0.05493729039741921), np.float64(0.0511788839583555), np.float64(0.045244046346952844), np.float64(0.04393085094753873), np.float64(0.04231539075785287), np.float64(0.04267081350080078), np.float64(0.043703929368423225), np.float64(0.04540910235097665), np.float64(0.0470106249936729), np.float64(0.04851468409743678), np.float64(0.05043018529306498), np.float64(0.0523421542658312), np.float64(0.05425517936117252), np.float64(0.05616075975764224), np.float64(0.05806634028354059), np.float64(0.05997192080734409), np.float64(0.06187750133100498), np.float64(0.06378308185470284), np.float64(0.06568866237840348)]
MSE: 19.145544655992236
MAE: 4.375538273320696
RMSE: 4.375562210275639
R²: 0.0
MAPE: 101.21583085836441%

Resultados para At con ventana 14:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.02850165694401747), np.float64(0.031828707456130555), np.float64(0.013315700225826795), np.float64(0.04618203804615304), np.float64(0.06566488278172859), np.float64(0.07506609787221218), np.float64(0.08185428916815615), np.float64(0.07644556723390318), np.float64(0.06533253101918013), np.float64(0.05493729039741921), np.float64(0.0511788839583555), np.float64(0.045244046346952844), np.float64(0.04393085094753873), np.float64(0.04231539075785287), np.float64(0.04267081350080078), np.float64(0.043703929368423225), np.float64(0.04540910235097665), np.float64(0.0470106249936729), np.float64(0.04851468409743678), np.float64(0.05043018529306498), np.float64(0.0523421542658312), np.float64(0.05425517936117252), np.float64(0.05616075975764224), np.float64(0.05806634028354059), np.float64(0.05997192080734409), np.float64(0.06187750133100498), np.float64(0.06378308185470284), np.float64(0.06568866237840348)]
MSE: 19.145544655992236
MAE: 4.375538273320696
RMSE: 4.375562210275639
R²: 0.0
MAPE: 101.21583085836441%

Resultados para At con ventana 21:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.02850165694401747), np.float64(0.031828707456130555), np.float64(0.013315700225826795), np.float64(0.04618203804615304), np.float64(0.06566488278172859), np.float64(0.07506609787221218), np.float64(0.08185428916815615), np.float64(0.07644556723390318), np.float64(0.06533253101918013), np.float64(0.05493729039741921), np.float64(0.0511788839583555), np.float64(0.045244046346952844), np.float64(0.04393085094753873), np.float64(0.04231539075785287), np.float64(0.04267081350080078), np.float64(0.043703929368423225), np.float64(0.04540910235097665), np.float64(0.0470106249936729), np.float64(0.04851468409743678), np.float64(0.05043018529306498), np.float64(0.0523421542658312), np.float64(0.05425517936117252), np.float64(0.05616075975764224), np.float64(0.05806634028354059), np.float64(0.05997192080734409), np.float64(0.06187750133100498), np.float64(0.06378308185470284), np.float64(0.06568866237840348)]
MSE: 19.145544655992236
MAE: 4.375538273320696
RMSE: 4.375562210275639
R²: 0.0
MAPE: 101.21583085836441%

Resultados para At con ventana 28:
Modelo ARIMA(p=2, d=2, q=5)
Predicciones: [np.float64(0.02850165694401747), np.float64(0.031828707456130555), np.float64(0.013315700225826795), np.float64(0.04618203804615304), np.float64(0.06566488278172859), np.float64(0.07506609787221218), np.float64(0.08185428916815615), np.float64(0.07644556723390318), np.float64(0.06533253101918013), np.float64(0.05493729039741921), np.float64(0.0511788839583555), np.float64(0.045244046346952844), np.float64(0.04393085094753873), np.float64(0.04231539075785287), np.float64(0.04267081350080078), np.float64(0.043703929368423225), np.float64(0.04540910235097665), np.float64(0.0470106249936729), np.float64(0.04851468409743678), np.float64(0.05043018529306498), np.float64(0.0523421542658312), np.float64(0.05425517936117252), np.float64(0.05616075975764224), np.float64(0.05806634028354059), np.float64(0.05997192080734409), np.float64(0.06187750133100498), np.float64(0.06378308185470284), np.float64(0.06568866237840348)]
MSE: 19.145544655992236
MAE: 4.375538273320696
RMSE: 4.375562210275639
R²: 0.0
MAPE: 101.21583085836441%

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.graphics.gofplots import qqplot
from statsmodels.tsa.stattools import acf
from statsmodels.stats.diagnostic import acorr_ljungbox

# Función para calcular métricas sobre los residuos
def calcular_metricas_residuos(y_true, y_pred):
    residuals = y_true - y_pred
    mse = mean_squared_error(y_true, y_pred)
    mae = mean_absolute_error(y_true, y_pred)
    rmse = np.sqrt(mse)
    r2 = r2_score(y_true, y_pred)
    mape = mean_absolute_percentage_error(y_true, y_pred)
    return mse, mae, rmse, r2, mape, residuals

# Crear un DataFrame vacío para almacenar las métricas y pruebas de hipótesis
resultados_df = pd.DataFrame(columns=['Variable', 'Ventana', 'MAPE', 'MAE', 'RMSE', 'MSE', 'R2', 
                                      'Ljung-Box p-value', 'Jarque-Bera p-value'])

# Para cada variable y cada ventana
for variable in predicciones:
    for ventana in predicciones[variable]:
        # Obtener predicciones y valores reales del conjunto de validación
        y_valid_true = df[variable].iloc[train_size:].values  # Valores reales de validación
        y_valid_pred = predicciones[variable][ventana]['predictions']  # Predicciones para la validación

        # Cálculo de las métricas y los residuos
        mse, mae, rmse, r2, mape, residuals = calcular_metricas_residuos(y_valid_true, y_valid_pred)

        # Pruebas de hipótesis
        ljung_box_pvalue = acorr_ljungbox(residuals, lags=[10], return_df=True)['lb_pvalue'].values[0]
        jb_test_pvalue = jarque_bera(residuals)[1]

        # Crear un nuevo DataFrame para agregar a resultados_df
        nuevo_resultado = pd.DataFrame({
            'Variable': [variable],
            'Ventana': [ventana],
            'MAPE': [mape],
            'MAE': [mae],
            'RMSE': [rmse],
            'MSE': [mse],
            'R2': [r2],
            'Ljung-Box p-value': [ljung_box_pvalue],
            'Jarque-Bera p-value': [jb_test_pvalue]
        })

        # Concatenar el nuevo resultado al DataFrame existente
        resultados_df = pd.concat([resultados_df, nuevo_resultado], ignore_index=True)

        # Visualización de los residuos

        # 1. Serie de residuos
        plt.figure(figsize=(10, 4))
        plt.plot(residuals, label=f'Residuals - {variable} (Ventana {ventana})')
        plt.title(f'Serie de Residuos - {variable} (Ventana {ventana})')
        plt.xlabel('Tiempo')
        plt.ylabel('Residuos')
        plt.legend()
        plt.show()

        # 2. QQ-Plot para la normalidad
        qqplot(residuals, line='s')
        plt.title(f'QQ-Plot - {variable} (Ventana {ventana})')
        plt.show()

        # 3. ACF de residuos
        plt.figure(figsize=(10, 4))
        acf_values = acf(residuals, fft=False)
        sns.barplot(x=np.arange(len(acf_values)), y=acf_values)
        plt.title(f'ACF de Residuos - {variable} (Ventana {ventana})')
        plt.xlabel('Rezagos')
        plt.ylabel('Autocorrelación')
        plt.show()

# Mostrar la tabla de resultados
print(resultados_df)

          Variable Ventana          MAPE           MAE          RMSE  \
0            Price       7  6.687065e+07  66870.645307  66918.947961   
1            Price      14  6.687065e+07  66870.645307  66918.947961   
2            Price      21  6.687065e+07  66870.645307  66918.947961   
3            Price      28  6.687065e+07  66870.645307  66918.947961   
4   Volatilidad_14       7           inf      0.027106      0.027477   
5   Volatilidad_14      14           inf      0.027106      0.027477   
6   Volatilidad_14      21           inf      0.027106      0.027477   
7   Volatilidad_14      28           inf      0.027106      0.027477   
8               At       7  1.012158e+02      4.375538      4.375562   
9               At      14  1.012158e+02      4.375538      4.375562   
10              At      21  1.012158e+02      4.375538      4.375562   
11              At      28  1.012158e+02      4.375538      4.375562   

             MSE            R2  Ljung-Box p-value  Jarque-Bera p-value  
0   4.478146e+09 -2.325186e+43       7.209159e-14             0.543975  
1   4.478146e+09 -2.325186e+43       7.209159e-14             0.543975  
2   4.478146e+09 -2.325186e+43       7.209159e-14             0.543975  
3   4.478146e+09 -2.325186e+43       7.209159e-14             0.543975  
4   7.550049e-04  0.000000e+00       5.932280e-16             0.375548  
5   7.550049e-04  0.000000e+00       5.932280e-16             0.375548  
6   7.550049e-04  0.000000e+00       5.932280e-16             0.375548  
7   7.550049e-04  0.000000e+00       5.932280e-16             0.375548  
8   1.914554e+01  0.000000e+00       3.829808e-07             0.645914  
9   1.914554e+01  0.000000e+00       3.829808e-07             0.645914  
10  1.914554e+01  0.000000e+00       3.829808e-07             0.645914  
11  1.914554e+01  0.000000e+00       3.829808e-07             0.645914  

Variable	Ventana	MAPE	MAE	RMSE	MSE	R²	Ljung-Box p-value	Jarque-Bera p-value
Price	7	6.687065e+07	66870.645307	66918.947961	4.478146e+09	-2.325186e+43	7.209159e-14	0.543975
Volatilidad_14	7	inf	0.027106	0.027477	7.550049e-04	0.000000e+00	5.932280e-16	0.375548
At	7	1.012158e+02	4.375538	4.375562	1.914554e+01	0.000000e+00	3.829808e-07	0.645914

Al analizar los resultados del modelo ARIMA aplicado a los precios de Bitcoin utilizando un enfoque de rolling, se observan varias métricas clave que indican el desempeño del modelo.

En primer lugar, el MAPE para Price es extremadamente alto (6.687065e+07), lo que sugiere que el modelo no es efectivo en la predicción de los precios. Además, la presencia de inf para Volatilidad_14 indica que el modelo no pudo realizar predicciones significativas para esta variable, posiblemente debido a la falta de datos o a una alta variabilidad. En cuanto al MAE, el valor para Price (66870.645307) es considerablemente alto, lo que refuerza la idea de que el modelo presenta grandes errores en sus predicciones. Por otro lado, el MAE para Volatilidad_14 es bajo, lo que sugiere que el modelo pudo predecir esta variable con un error relativamente pequeño.

El RMSE también muestra un resultado desfavorable para Price (66918.947961), indicando que el modelo tiene un desempeño deficiente en esta variable. Aunque el RMSE para Volatilidad_14 y At es bajo, lo que sugiere que el modelo puede captar algunas tendencias, la falta de predicciones significativas limita su utilidad.

En cuanto al MSE, el valor para Price (4.478146e+09) es alto, lo que refuerza la idea de que las predicciones son inexactas. Los valores de Volatilidad_14 y At son bajos, lo que podría indicar un mejor desempeño del modelo en estas variables, aunque hay que tener en cuenta las problemáticas en el MAPE.

El R² para Price es negativo (-2.325186e+43), lo que indica que el modelo no explica ninguna varianza en los datos y se comporta peor que una simple media. Los R² de 0 para Volatilidad_14 y At sugieren que el modelo no puede explicar la varianza de estas variables en absoluto, lo que refuerza la idea de que el modelo ARIMA puede no ser adecuado para estas predicciones.

Por último, al revisar las pruebas de residuos, el p-value de Ljung-Box para Price (7.209159e-14) indica problemas de autocorrelación, lo cual también se observa en Volatilidad_14 (5.932280e-16) y At (3.829808e-07). Esto sugiere que el modelo no está capturando completamente la dinámica de los datos. Además, aunque el p-value de Jarque-Bera es relativamente alto para Price, en general sugiere que los residuos no se distribuyen normalmente.

En conclusión, el modelo ARIMA presenta un rendimiento deficiente al predecir los precios de Bitcoin, evidenciado por métricas de error extremadamente altas y un R² negativo. Aunque las métricas para Volatilidad_14 y At indican un mejor rendimiento, siguen siendo problemáticas. Será necesario explorar otros modelos, ajustar los parámetros del ARIMA o considerar técnicas más complejas de aprendizaje automático para mejorar la predicción. También es crucial revisar los residuos para entender la naturaleza de los errores y ajustar el modelo en consecuencia.

Analisis graficos

Al analizar los gráficos de QQ plot, ACF y residuos en el tiempo para el modelo Arima con rolling aplicado a las variables Price, Volatilidad y Retornos acumulados, se pueden observar patrones consistentes y algunos desafíos en el ajuste del modelo, especialmente en términos de normalidad y autocorrelación.

Para los gráficos de Price, el QQ plot muestra una clara separación sinusoidal de los puntos con respecto a la línea roja, lo cual indica que los residuos no se ajustan bien a una distribución normal y presentan algún tipo de patrón recurrente. En los residuos a través del tiempo, observo un aumento lineal conforme pasa el tiempo, lo que sugiere una posible tendencia o falta de estacionariedad en los errores. Esta tendencia en los residuos podría indicar que el modelo Arima no está capturando adecuadamente la volatilidad de largo plazo en la variable Price. Además, el gráfico ACF muestra una estructura de “espina” decreciente con muchos rezagos por fuera de la banda de significancia, lo que señala una autocorrelación significativa en los residuos. Esto implica que el modelo está dejando patrones de dependencia temporal sin capturar, algo que debe ser ajustado para mejorar la precisión.

Para los gráficos de Volatilidad, el patrón es similar, aunque con algunas particularidades. En el QQ plot, los puntos también se separan significativamente de la línea de referencia en una forma sinusoidal, lo cual sigue sugiriendo problemas de normalidad en los residuos. Al observar los residuos en el tiempo, encuentro que estos presentan una caída inicial, seguida de un crecimiento lineal a medida que transcurre el tiempo, lo que podría reflejar cierta estructura que el modelo no logra capturar correctamente, ya sea en los periodos de aumento o de caída de la volatilidad. En el ACF, la estructura en “espina” es visible nuevamente, con muchos rezagos fuera de las bandas de significancia. Esta autocorrelación persistente sugiere que el modelo GARCH no está capturando totalmente las variaciones de la volatilidad, lo cual podría afectar la estabilidad y fiabilidad de las predicciones.

En cuanto a los gráficos de Retornos acumulados, el patrón es un poco más ajustado. En el QQ plot, los puntos están solo ligeramente separados de la línea roja, lo que indica que la normalidad de los residuos es menos problemática aquí en comparación con las otras variables. Los residuos a través del tiempo muestran una leve variación: primero un pico, luego una caída, y posteriormente una oscilación constante dentro de un intervalo determinado. Esto sugiere una mayor estabilidad en los residuos de Retornos acumulados, lo que indica que el modelo captura mejor las dinámicas de esta variable en particular. En el gráfico ACF, se observa una estructura en “espina” pero con pocos rezagos fuera de las bandas de significancia, lo que indica una autocorrelación menos persistente en comparación con Price y Volatilidad.

# Crear un DataFrame vacío para almacenar las métricas y pruebas de hipótesis
resultados_test_df = pd.DataFrame(columns=['Variable', 'Ventana', 'MAPE', 'MAE', 'RMSE', 'MSE', 'R2', 
                                           'Ljung-Box p-value'])

# Para cada variable y cada ventana
for variable in predicciones:
    for ventana in predicciones[variable]:
        # Obtener predicciones y valores reales del conjunto de validación
        y_valid_true = df[variable].iloc[train_size:].values  # Valores reales de validación
        y_valid_pred = predicciones[variable][ventana]['predictions']  # Predicciones para la validación

        # Calcular las métricas de error
        mse = mean_squared_error(y_valid_true, y_valid_pred)
        mae = mean_absolute_error(y_valid_true, y_valid_pred)
        rmse = np.sqrt(mse)
        r2 = r2_score(y_valid_true, y_valid_pred)
        mape = mean_absolute_percentage_error(y_valid_true, y_valid_pred)

        # Pruebas de hipótesis
        residuals = y_valid_true - y_valid_pred
        ljung_box_pvalue = acorr_ljungbox(residuals, lags=[10], return_df=True)['lb_pvalue'].values[0]

        # Crear un nuevo DataFrame para agregar a resultados_test_df
        nuevo_resultado_test = pd.DataFrame({
            'Variable': [variable],
            'Ventana': [ventana],
            'MAPE': [mape],
            'MAE': [mae],
            'RMSE': [rmse],
            'MSE': [mse],
            'R2': [r2],
            'Ljung-Box p-value': [ljung_box_pvalue]
        })

        # Concatenar el nuevo resultado al DataFrame existente
        resultados_test_df = pd.concat([resultados_test_df, nuevo_resultado_test], ignore_index=True)

# Mostrar la tabla de resultados en el conjunto de test
print(resultados_test_df)

          Variable Ventana          MAPE           MAE          RMSE  \
0            Price       7  6.687065e+07  66870.645307  66918.947961   
1            Price      14  6.687065e+07  66870.645307  66918.947961   
2            Price      21  6.687065e+07  66870.645307  66918.947961   
3            Price      28  6.687065e+07  66870.645307  66918.947961   
4   Volatilidad_14       7           inf      0.027106      0.027477   
5   Volatilidad_14      14           inf      0.027106      0.027477   
6   Volatilidad_14      21           inf      0.027106      0.027477   
7   Volatilidad_14      28           inf      0.027106      0.027477   
8               At       7  1.012158e+02      4.375538      4.375562   
9               At      14  1.012158e+02      4.375538      4.375562   
10              At      21  1.012158e+02      4.375538      4.375562   
11              At      28  1.012158e+02      4.375538      4.375562   

             MSE            R2  Ljung-Box p-value  
0   4.478146e+09 -2.325186e+43       7.209159e-14  
1   4.478146e+09 -2.325186e+43       7.209159e-14  
2   4.478146e+09 -2.325186e+43       7.209159e-14  
3   4.478146e+09 -2.325186e+43       7.209159e-14  
4   7.550049e-04  0.000000e+00       5.932280e-16  
5   7.550049e-04  0.000000e+00       5.932280e-16  
6   7.550049e-04  0.000000e+00       5.932280e-16  
7   7.550049e-04  0.000000e+00       5.932280e-16  
8   1.914554e+01  0.000000e+00       3.829808e-07  
9   1.914554e+01  0.000000e+00       3.829808e-07  
10  1.914554e+01  0.000000e+00       3.829808e-07  
11  1.914554e+01  0.000000e+00       3.829808e-07  

Variable	Ventana	MAPE	MAE	RMSE	MSE	R2	Ljung-Box p-value
Price	7	6.965060e+07	69650.602424	69655.160162	4.851841e+09	-2.519220e+43	0.000019
Price	14	6.965060e+07	69650.602424	69655.160162	4.851841e+09	-2.519220e+43	0.000019
Price	21	6.965060e+07	69650.602424	69655.160162	4.851841e+09	-2.519220e+43	0.000019
Price	28	6.965060e+07	69650.602424	69655.160162	4.851841e+09	-2.519220e+43	0.000019
Volatilidad_14	7	inf	0.038262	0.038262	1.463995e-03	0.000000e+00	0.123431
Volatilidad_14	14	inf	0.038262	0.038262	1.463995e-03	0.000000e+00	0.123431
Volatilidad_14	21	inf	0.038262	0.038262	1.463995e-03	0.000000e+00	0.123431
Volatilidad_14	28	inf	0.038262	0.038262	1.463995e-03	0.000000e+00	0.123431
At	7	1.006525e+02	4.351187	4.351191	1.893286e+01	0.000000e+00	0.397909
At	14	1.006525e+02	4.351187	4.351191	1.893286e+01	0.000000e+00	0.397909
At	21	1.006525e+02	4.351187	4.351191	1.893286e+01	0.000000e+00	0.397909
At	28	1.006525e+02	4.351187	4.351191	1.893286e+01	0.000000e+00	0.397909

Al analizar los residuos de la predicción de mi modelo ARIMA con rolling para los precios de Bitcoin, observé varios aspectos importantes que merecen atención. En primer lugar, la distribución de los residuos muestra un comportamiento que se desvía de la normalidad, lo cual es evidente en la prueba de Jarque-Bera, donde el valor p es significativamente menor a 0.05. Esto sugiere que los residuos no se distribuyen normalmente, lo que podría indicar la presencia de heterocedasticidad o patrones en los errores que el modelo no ha capturado adecuadamente.

Además, la prueba de Ljung-Box también presenta valores p bajos, lo que sugiere que hay autocorrelación significativa en los residuos. Este resultado implica que los residuos no son completamente aleatorios y que el modelo puede no estar capturando todas las dinámicas presentes en la serie temporal de los precios de Bitcoin. La autocorrelación en los residuos puede ser problemática, ya que puede afectar la validez de las predicciones y la interpretación de los resultados.

En cuanto a los residuos en sí, se observa que en algunos periodos presentan grandes desviaciones, lo que indica que el modelo subestima o sobreestima los precios en esos momentos específicos. Este comportamiento es preocupante, ya que sugiere que el modelo podría ser sensible a eventos extremos o cambios abruptos en el mercado, algo común en la volatilidad del precio de Bitcoin.

Arima sin Rolling

import pandas as pd
import numpy as np
import warnings  # Para suprimir advertencias
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.stats.diagnostic import acorr_ljungbox

# Suprimir advertencias de convergencia
warnings.filterwarnings("ignore", message=".*Maximum Likelihood optimization failed to converge.*")
warnings.filterwarnings("ignore", message=".*Non-stationary starting autoregressive parameters found.*")
warnings.filterwarnings("ignore", message=".*Non-invertible starting MA parameters found.*")

# Función para calcular MAPE
def mean_absolute_percentage_error(y_true, y_pred):
    y_true, y_pred = np.array(y_true), np.array(y_pred)
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Parámetros
ventanas = [7, 14, 21, 28]  # Ventanas de predicción
variables = ['Price', 'Volatilidad_14', 'At']

# Almacenaremos las predicciones y métricas
predicciones = {}

# Dividimos el conjunto de validación y entrenamiento
train_size = len(df) - 28
test_size = 28

# Para cada variable y cada ventana
for variable in variables:
    predicciones[variable] = {}

    # Tomamos el conjunto de entrenamiento para esa variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    for ventana in ventanas:
        # Definir parámetros ARIMA
        p, d, q = 4, 2, 2  # Puedes ajustar estos parámetros según necesidad

        # Ajustar el modelo ARIMA al conjunto de entrenamiento
        model = ARIMA(train_series, order=(p, d, q))
        model_fit = model.fit()

        # Hacer predicciones en el conjunto de validación
        val_predictions = model_fit.forecast(steps=test_size)

        # Guardar las predicciones
        predicciones[variable][ventana] = {
            'predictions': val_predictions,
        }

        # Evaluar en el conjunto de validación
        y_true = df[variable].iloc[train_size:].values  # Valores reales de validación

        # Métricas de error
        mse = mean_squared_error(y_true, val_predictions)
        mae = mean_absolute_error(y_true, val_predictions)
        rmse = np.sqrt(mse)  # RMSE es la raíz cuadrada del MSE
        r2 = r2_score(y_true, val_predictions)
        mape = mean_absolute_percentage_error(y_true, val_predictions)

        # Guardar las métricas en el diccionario
        predicciones[variable][ventana]['mse'] = mse
        predicciones[variable][ventana]['mae'] = mae
        predicciones[variable][ventana]['rmse'] = rmse
        predicciones[variable][ventana]['r2'] = r2
        predicciones[variable][ventana]['mape'] = mape

        # Calcular residuos para pruebas de hipótesis
        residuals = y_true - val_predictions
        ljung_box_pvalue = acorr_ljungbox(residuals, lags=[10], return_df=True)['lb_pvalue'].values[0]

        # Guardar el p-value de Ljung-Box
        predicciones[variable][ventana]['Ljung-Box p-value'] = ljung_box_pvalue

        # Mostrar los resultados del modelo actual
        print(f"\nResultados para {variable} con ventana {ventana}:")
        print(f"Modelo ARIMA(p={p}, d={d}, q={q})")
        print(f"MSE: {predicciones[variable][ventana]['mse']}")
        print(f"MAE: {predicciones[variable][ventana]['mae']}")
        print(f"RMSE: {predicciones[variable][ventana]['rmse']}")
        print(f"R²: {predicciones[variable][ventana]['r2']}")
        print(f"MAPE: {predicciones[variable][ventana]['mape']}%")
        print(f"Ljung-Box p-value: {predicciones[variable][ventana]['Ljung-Box p-value']}")

# Crear un DataFrame para almacenar los resultados
resultados_df = pd.DataFrame(columns=['Variable', 'Ventana', 'MAPE', 'MAE', 'RMSE', 'MSE', 'R2', 'Ljung-Box p-value'])

# Agregar los resultados al DataFrame usando pd.concat
resultados = []
for variable in predicciones:
    for ventana in predicciones[variable]:
        resultados.append({
            'Variable': variable,
            'Ventana': ventana,
            'MAPE': predicciones[variable][ventana]['mape'],
            'MAE': predicciones[variable][ventana]['mae'],
            'RMSE': predicciones[variable][ventana]['rmse'],
            'MSE': predicciones[variable][ventana]['mse'],
            'R2': predicciones[variable][ventana]['r2'],
            'Ljung-Box p-value': predicciones[variable][ventana]['Ljung-Box p-value']
        })

resultados_df = pd.concat([resultados_df, pd.DataFrame(resultados)], ignore_index=True)

# Mostrar la tabla de resultados
print("\nResultados del modelo ARIMA sin rolling por ventana:")
print(resultados_df)

Resultados para Price con ventana 7:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 21044.888928204677
MAE: 126.34251528027868
RMSE: 145.06856629954223
R²: -1.0927131067013152e+38
MAPE: 126342.51528027869%
Ljung-Box p-value: 3.4924553224656613e-15

Resultados para Price con ventana 14:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 21044.888928204677
MAE: 126.34251528027868
RMSE: 145.06856629954223
R²: -1.0927131067013152e+38
MAPE: 126342.51528027869%
Ljung-Box p-value: 3.4924553224656613e-15

Resultados para Price con ventana 21:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 21044.888928204677
MAE: 126.34251528027868
RMSE: 145.06856629954223
R²: -1.0927131067013152e+38
MAPE: 126342.51528027869%
Ljung-Box p-value: 3.4924553224656613e-15

Resultados para Price con ventana 28:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 21044.888928204677
MAE: 126.34251528027868
RMSE: 145.06856629954223
R²: -1.0927131067013152e+38
MAPE: 126342.51528027869%
Ljung-Box p-value: 3.4924553224656613e-15

Resultados para Volatilidad_14 con ventana 7:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 2.975040610827173e-06
MAE: 0.0014759497419969297
RMSE: 0.0017248306035165231
R²: 0.0
MAPE: inf%
Ljung-Box p-value: 4.114540392979744e-15

Resultados para Volatilidad_14 con ventana 14:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 2.975040610827173e-06
MAE: 0.0014759497419969297
RMSE: 0.0017248306035165231
R²: 0.0
MAPE: inf%
Ljung-Box p-value: 4.114540392979744e-15

Resultados para Volatilidad_14 con ventana 21:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 2.975040610827173e-06
MAE: 0.0014759497419969297
RMSE: 0.0017248306035165231
R²: 0.0
MAPE: inf%
Ljung-Box p-value: 4.114540392979744e-15

Resultados para Volatilidad_14 con ventana 28:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 2.975040610827173e-06
MAE: 0.0014759497419969297
RMSE: 0.0017248306035165231
R²: 0.0
MAPE: inf%
Ljung-Box p-value: 4.114540392979744e-15

Resultados para At con ventana 7:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 0.0005597582398508827
MAE: 0.02077438236890356
RMSE: 0.023659210465501224
R²: 0.0
MAPE: 0.48055718878266074%
Ljung-Box p-value: 3.974194546292464e-15

Resultados para At con ventana 14:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 0.0005597582398508827
MAE: 0.02077438236890356
RMSE: 0.023659210465501224
R²: 0.0
MAPE: 0.48055718878266074%
Ljung-Box p-value: 3.974194546292464e-15

Resultados para At con ventana 21:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 0.0005597582398508827
MAE: 0.02077438236890356
RMSE: 0.023659210465501224
R²: 0.0
MAPE: 0.48055718878266074%
Ljung-Box p-value: 3.974194546292464e-15

Resultados para At con ventana 28:
Modelo ARIMA(p=4, d=2, q=2)
MSE: 0.0005597582398508827
MAE: 0.02077438236890356
RMSE: 0.023659210465501224
R²: 0.0
MAPE: 0.48055718878266074%
Ljung-Box p-value: 3.974194546292464e-15

Resultados del modelo ARIMA sin rolling por ventana:
          Variable Ventana          MAPE         MAE        RMSE  \
0            Price       7  1.263425e+05  126.342515  145.068566   
1            Price      14  1.263425e+05  126.342515  145.068566   
2            Price      21  1.263425e+05  126.342515  145.068566   
3            Price      28  1.263425e+05  126.342515  145.068566   
4   Volatilidad_14       7           inf    0.001476    0.001725   
5   Volatilidad_14      14           inf    0.001476    0.001725   
6   Volatilidad_14      21           inf    0.001476    0.001725   
7   Volatilidad_14      28           inf    0.001476    0.001725   
8               At       7  4.805572e-01    0.020774    0.023659   
9               At      14  4.805572e-01    0.020774    0.023659   
10              At      21  4.805572e-01    0.020774    0.023659   
11              At      28  4.805572e-01    0.020774    0.023659   

             MSE            R2  Ljung-Box p-value  
0   21044.888928 -1.092713e+38       3.492455e-15  
1   21044.888928 -1.092713e+38       3.492455e-15  
2   21044.888928 -1.092713e+38       3.492455e-15  
3   21044.888928 -1.092713e+38       3.492455e-15  
4       0.000003  0.000000e+00       4.114540e-15  
5       0.000003  0.000000e+00       4.114540e-15  
6       0.000003  0.000000e+00       4.114540e-15  
7       0.000003  0.000000e+00       4.114540e-15  
8       0.000560  0.000000e+00       3.974195e-15  
9       0.000560  0.000000e+00       3.974195e-15  
10      0.000560  0.000000e+00       3.974195e-15  
11      0.000560  0.000000e+00       3.974195e-15  

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.graphics.gofplots import qqplot
from statsmodels.tsa.stattools import acf
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.stats.stattools import jarque_bera  # Asegúrate de importar esta función

# Función para calcular métricas sobre los residuos
def calcular_metricas_residuos(y_true, y_pred):
    residuals = y_true - y_pred
    mse = mean_squared_error(y_true, y_pred)
    mae = mean_absolute_error(y_true, y_pred)
    rmse = np.sqrt(mse)
    r2 = r2_score(y_true, y_pred)
    mape = mean_absolute_percentage_error(y_true, y_pred)
    return mse, mae, rmse, r2, mape, residuals

# Crear un DataFrame vacío para almacenar las métricas y pruebas de hipótesis
resultados_df = pd.DataFrame(columns=['Variable', 'Ventana', 'MAPE', 'MAE', 'RMSE', 'MSE', 'R2', 
                                      'Ljung-Box p-value', 'Jarque-Bera p-value'])

# Para cada variable y cada ventana
for variable in variables:
    for ventana in ventanas:
        # Obtener predicciones y valores reales del conjunto de validación
        y_valid_true = df[variable].iloc[train_size:].values  # Valores reales de validación
        y_valid_pred = predicciones[variable][ventana]['predictions']  # Predicciones para la validación

        # Cálculo de las métricas y los residuos
        mse, mae, rmse, r2, mape, residuals = calcular_metricas_residuos(y_valid_true, y_valid_pred)

        # Pruebas de hipótesis
        ljung_box_pvalue = acorr_ljungbox(residuals, lags=[10], return_df=True)['lb_pvalue'].values[0]
        jb_test_pvalue = jarque_bera(residuals)[1]

        # Crear un nuevo DataFrame para agregar a resultados_df
        nuevo_resultado = pd.DataFrame({
            'Variable': [variable],
            'Ventana': [ventana],
            'MAPE': [mape],
            'MAE': [mae],
            'RMSE': [rmse],
            'MSE': [mse],
            'R2': [r2],
            'Ljung-Box p-value': [ljung_box_pvalue],
            'Jarque-Bera p-value': [jb_test_pvalue]
        })

        # Concatenar el nuevo resultado al DataFrame existente
        resultados_df = pd.concat([resultados_df, nuevo_resultado], ignore_index=True)

        # Visualización de los residuos

        # 1. Serie de residuos
        plt.figure(figsize=(10, 4))
        plt.plot(residuals, label=f'Residuals - {variable} (Ventana {ventana})')
        plt.title(f'Serie de Residuos - {variable} (Ventana {ventana})')
        plt.xlabel('Tiempo')
        plt.ylabel('Residuos')
        plt.legend()
        plt.show()

        # 2. QQ-Plot para la normalidad
        qqplot(residuals, line='s')
        plt.title(f'QQ-Plot - {variable} (Ventana {ventana})')
        plt.show()

        # 3. ACF de residuos
        plt.figure(figsize=(10, 4))
        acf_values = acf(residuals, fft=False)
        sns.barplot(x=np.arange(len(acf_values)), y=acf_values)
        plt.title(f'ACF de Residuos - {variable} (Ventana {ventana})')
        plt.xlabel('Rezagos')
        plt.ylabel('Autocorrelación')
        plt.show()

# Mostrar la tabla de resultados
print(resultados_df)

          Variable Ventana          MAPE         MAE        RMSE  \
0            Price       7  1.263425e+05  126.342515  145.068566   
1            Price      14  1.263425e+05  126.342515  145.068566   
2            Price      21  1.263425e+05  126.342515  145.068566   
3            Price      28  1.263425e+05  126.342515  145.068566   
4   Volatilidad_14       7           inf    0.001476    0.001725   
5   Volatilidad_14      14           inf    0.001476    0.001725   
6   Volatilidad_14      21           inf    0.001476    0.001725   
7   Volatilidad_14      28           inf    0.001476    0.001725   
8               At       7  4.805572e-01    0.020774    0.023659   
9               At      14  4.805572e-01    0.020774    0.023659   
10              At      21  4.805572e-01    0.020774    0.023659   
11              At      28  4.805572e-01    0.020774    0.023659   

             MSE            R2  Ljung-Box p-value  Jarque-Bera p-value  
0   21044.888928 -1.092713e+38       3.492455e-15             0.427166  
1   21044.888928 -1.092713e+38       3.492455e-15             0.427166  
2   21044.888928 -1.092713e+38       3.492455e-15             0.427166  
3   21044.888928 -1.092713e+38       3.492455e-15             0.427166  
4       0.000003  0.000000e+00       4.114540e-15             0.431674  
5       0.000003  0.000000e+00       4.114540e-15             0.431674  
6       0.000003  0.000000e+00       4.114540e-15             0.431674  
7       0.000003  0.000000e+00       4.114540e-15             0.431674  
8       0.000560  0.000000e+00       3.974195e-15             0.431853  
9       0.000560  0.000000e+00       3.974195e-15             0.431853  
10      0.000560  0.000000e+00       3.974195e-15             0.431853  
11      0.000560  0.000000e+00       3.974195e-15             0.431853  

import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox

# Crear un DataFrame vacío para almacenar las métricas y pruebas de hipótesis
resultados_test_df = pd.DataFrame(columns=['Variable', 'Ventana', 'MAPE', 'MAE', 'RMSE', 'MSE', 'R2', 
                                           'Ljung-Box p-value'])

# Para cada variable y cada ventana
for variable in variables:
    for ventana in ventanas:
        # Obtener predicciones y valores reales del conjunto de validación
        y_valid_true = df[variable].iloc[train_size:].values  # Valores reales de validación
        y_valid_pred = predicciones[variable][ventana]['predictions']  # Predicciones para la validación

        # Calcular las métricas de error
        mse = mean_squared_error(y_valid_true, y_valid_pred)
        mae = mean_absolute_error(y_valid_true, y_valid_pred)
        rmse = np.sqrt(mse)
        r2 = r2_score(y_valid_true, y_valid_pred)
        mape = mean_absolute_percentage_error(y_valid_true, y_valid_pred)

        # Calcular los residuos y realizar la prueba de Ljung-Box
        residuals = y_valid_true - y_valid_pred
        ljung_box_pvalue = acorr_ljungbox(residuals, lags=[10], return_df=True)['lb_pvalue'].values[0]

        # Crear un nuevo DataFrame para agregar a resultados_test_df
        nuevo_resultado_test = pd.DataFrame({
            'Variable': [variable],
            'Ventana': [ventana],
            'MAPE': [mape],
            'MAE': [mae],
            'RMSE': [rmse],
            'MSE': [mse],
            'R2': [r2],
            'Ljung-Box p-value': [ljung_box_pvalue]
        })

        # Concatenar el nuevo resultado al DataFrame existente
        resultados_test_df = pd.concat([resultados_test_df, nuevo_resultado_test], ignore_index=True)

# Mostrar la tabla de resultados en el conjunto de test
print(resultados_test_df)

          Variable Ventana          MAPE           MAE          RMSE  \
0            Price       7  2.985947e-06  2.985947e-09  3.095757e-09   
1            Price      14  2.985947e-06  2.985947e-09  3.095757e-09   
2            Price      21  2.985947e-06  2.985947e-09  3.095757e-09   
3            Price      28  2.985947e-06  2.985947e-09  3.095757e-09   
4   Volatilidad_14       7           inf  6.353263e-06  6.623300e-06   
5   Volatilidad_14      14           inf  6.353263e-06  6.623300e-06   
6   Volatilidad_14      21           inf  6.353263e-06  6.623300e-06   
7   Volatilidad_14      28           inf  6.353263e-06  6.623300e-06   
8               At       7  7.286323e-13  3.149861e-14  3.189723e-14   
9               At      14  7.286323e-13  3.149861e-14  3.189723e-14   
10              At      21  7.286323e-13  3.149861e-14  3.189723e-14   
11              At      28  7.286323e-13  3.149861e-14  3.189723e-14   

             MSE            R2  Ljung-Box p-value  
0   9.583710e-18 -4.976147e+16       4.167894e-03  
1   9.583710e-18 -4.976147e+16       4.167894e-03  
2   9.583710e-18 -4.976147e+16       4.167894e-03  
3   9.583710e-18 -4.976147e+16       4.167894e-03  
4   4.386810e-11  0.000000e+00       8.055365e-19  
5   4.386810e-11  0.000000e+00       8.055365e-19  
6   4.386810e-11  0.000000e+00       8.055365e-19  
7   4.386810e-11  0.000000e+00       8.055365e-19  
8   1.017433e-27  0.000000e+00       8.145282e-02  
9   1.017433e-27  0.000000e+00       8.145282e-02  
10  1.017433e-27  0.000000e+00       8.145282e-02  
11  1.017433e-27  0.000000e+00       8.145282e-02  

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\3768060156.py:41: FutureWarning:

The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\1254920799.py:16: RuntimeWarning:

divide by zero encountered in divide

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\1254920799.py:16: RuntimeWarning:

divide by zero encountered in divide

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\1254920799.py:16: RuntimeWarning:

divide by zero encountered in divide

C:\Users\Maestriadatos\AppData\Local\Temp\ipykernel_11704\1254920799.py:16: RuntimeWarning:

divide by zero encountered in divide

Variable	Ventana	MAPE	MAE	RMSE	MSE	R2	Ljung-Box p-value	Jarque-Bera p-value
Price	7	1.263425e+05	126.342515	145.068566	21044.888928	-1.092713e+38	3.492455e-15	0.427166
Price	14	1.263425e+05	126.342515	145.068566	21044.888928	-1.092713e+38	3.492455e-15	0.427166
Price	21	1.263425e+05	126.342515	145.068566	21044.888928	-1.092713e+38	3.492455e-15	0.427166
Price	28	1.263425e+05	126.342515	145.068566	21044.888928	-1.092713e+38	3.492455e-15	0.427166
Volatilidad_14	7	inf	0.001476	0.001725	0.000003	0.000000e+00	4.114540e-15	0.431674
Volatilidad_14	14	inf	0.001476	0.001725	0.000003	0.000000e+00	4.114540e-15	0.431674
Volatilidad_14	21	inf	0.001476	0.001725	0.000003	0.000000e+00	4.114540e-15	0.431674
Volatilidad_14	28	inf	0.001476	0.001725	0.000003	0.000000e+00	4.114540e-15	0.431674
At	7	4.805572e-01	0.020774	0.023659	0.000560	0.000000e+00	3.974195e-15	0.431853
At	14	4.805572e-01	0.020774	0.023659	0.000560	0.000000e+00	3.974195e-15	0.431853
At	21	4.805572e-01	0.020774	0.023659	0.000560	0.000000e+00	3.974195e-15	0.431853
At	28	4.805572e-01	0.020774	0.023659	0.000560	0.000000e+00	3.974195e-15	0.431853

Al analizar los residuos del modelo ARIMA sin rolling para las variables Price, Volatilidad_14 y At en diferentes ventanas, se observa un comportamiento notable en las métricas de error y en las pruebas de autocorrelación y normalidad.

Para la variable Price, el MAPE muestra valores extremadamente altos (del orden de 1 0 5 10 5 ), indicando un error porcentual significativo. Las métricas MAE y RMSE también reflejan que los residuos presentan un error considerable. El MSE de más de 21044 y el R² negativo (- 1 0 38 10 38 ) sugieren que el modelo no está logrando capturar adecuadamente la variabilidad de la serie temporal en ninguna de las ventanas. Además, la prueba de Ljung-Box muestra un valor p muy bajo ( 3.49 × 1 0 − 15 3.49×10 −15 ), lo que indica autocorrelación significativa en los residuos. Sin embargo, la prueba de Jarque-Bera arroja un p-valor de 0.427, lo que sugiere que, pese a la autocorrelación, los residuos no se desvían notablemente de la normalidad.

En el caso de Volatilidad_14, el MAPE es infinito en todas las ventanas, probablemente debido a valores residuales extremadamente bajos que generan problemas al calcular el error porcentual. Aunque el MAE y RMSE son mínimos (0.0015 y 0.0017 respectivamente), el R² de cero indica que el modelo no logra explicar ninguna variación en los datos. Al igual que con la variable Price, los residuos de Volatilidad_14 presentan una autocorrelación significativa (p-valor de Ljung-Box de 4.11 × 1 0 − 15 4.11×10 −15 ), y el p-valor de Jarque-Bera (0.431) sugiere normalidad de los residuos.

Para At, el MAPE es bastante bajo (aproximadamente 0.48), lo que indica que el modelo tiene una precisión razonable para esta variable en términos de error porcentual. Sin embargo, las métricas de error absoluto y cuadrático (MAE y RMSE) junto con el R² de cero sugieren que el modelo aún no es capaz de explicar la variabilidad de At. Nuevamente, la prueba de Ljung-Box da un p-valor muy bajo ( 3.97 × 1 0 − 15 3.97×10 −15 ), lo que indica autocorrelación significativa, y la prueba de Jarque-Bera con p-valor de 0.431 muestra una tendencia hacia la normalidad en los residuos.

En resumen, estos residuos presentan autocorrelación en todas las variables y ventanas, lo que indica una limitación en el modelo ARIMA sin rolling para capturar la dinámica de estas series. Además, aunque los residuos son en su mayoría normales, la capacidad predictiva del modelo es baja, especialmente en Price y Volatilidad_14, mientras que At muestra un desempeño ligeramente mejor en términos de precisión porcentual. Estos hallazgos sugieren que se podría explorar un ajuste adicional del modelo o un enfoque alternativo para mejorar la captura de la dinámica de las series.

Analisis grafico

Al analizar los residuos del modelo ARIMA sin rolling para las variables Price, Volatilidad_14 y At en diferentes ventanas, se observa un comportamiento notable en las métricas de error y en las pruebas de autocorrelación y normalidad.

Para la variable Price, el MAPE muestra valores extremadamente altos (del orden de 1 0 5 10 5 ), indicando un error porcentual significativo. Las métricas MAE y RMSE también reflejan que los residuos presentan un error considerable. El MSE de más de 21044 y el R² negativo (- 1 0 38 10 38 ) sugieren que el modelo no está logrando capturar adecuadamente la variabilidad de la serie temporal en ninguna de las ventanas. Además, la prueba de Ljung-Box muestra un valor p muy bajo ( 3.49 × 1 0 − 15 3.49×10 −15 ), lo que indica autocorrelación significativa en los residuos. Sin embargo, la prueba de Jarque-Bera arroja un p-valor de 0.427, lo que sugiere que, pese a la autocorrelación, los residuos no se desvían notablemente de la normalidad.

En el caso de Volatilidad_14, el MAPE es infinito en todas las ventanas, probablemente debido a valores residuales extremadamente bajos que generan problemas al calcular el error porcentual. Aunque el MAE y RMSE son mínimos (0.0015 y 0.0017 respectivamente), el R² de cero indica que el modelo no logra explicar ninguna variación en los datos. Al igual que con la variable Price, los residuos de Volatilidad_14 presentan una autocorrelación significativa (p-valor de Ljung-Box de 4.11 × 1 0 − 15 4.11×10 −15 ), y el p-valor de Jarque-Bera (0.431) sugiere normalidad de los residuos.

Para At, el MAPE es bastante bajo (aproximadamente 0.48), lo que indica que el modelo tiene una precisión razonable para esta variable en términos de error porcentual. Sin embargo, las métricas de error absoluto y cuadrático (MAE y RMSE) junto con el R² de cero sugieren que el modelo aún no es capaz de explicar la variabilidad de At. Nuevamente, la prueba de Ljung-Box da un p-valor muy bajo ( 3.97 × 1 0 − 15 3.97×10 −15 ), lo que indica autocorrelación significativa, y la prueba de Jarque-Bera con p-valor de 0.431 muestra una tendencia hacia la normalidad en los residuos.

En resumen, estos residuos presentan autocorrelación en todas las variables y ventanas, lo que indica una limitación en el modelo ARIMA sin rolling para capturar la dinámica de estas series. Además, aunque los residuos son en su mayoría normales, la capacidad predictiva del modelo es baja, especialmente en Price y Volatilidad_14, mientras que At muestra un desempeño ligeramente mejor en términos de precisión porcentual. Estos hallazgos sugieren que se podría explorar un ajuste adicional del modelo o un enfoque alternativo para mejorar la captura de la dinámica de las series.

Garch con Rolling

import pandas as pd
import numpy as np
from arch import arch_model
from concurrent.futures import ThreadPoolExecutor
import warnings

# Suprimir warnings
warnings.filterwarnings("ignore")

# Parámetros generales
ventanas = [14, 28, 21, 7]  # Ventanas de rolling para todas las variables
step_size = 20  # Tamaño de paso para el rolling
train_size = len(df) - 28
test_size = 28

# Función para ejecutar el rolling de GARCH en paralelo
def ajustar_garch(variable, ventana, start, train_series):
    end = start + ventana
    rolling_train_series = train_series[start:end]
    
    # Ajustar el modelo GARCH(1,1)
    model = arch_model(rolling_train_series, vol='Garch', p=3, q=6)
    model_fit = model.fit(disp=False, tol=1e-4)  # Ajustar el modelo

    # Realizar predicciones
    forecast = model_fit.forecast(horizon=test_size)
    var_pred = forecast.variance.values[-1, :]  # Predicciones de varianza
    
    # Guardar predicciones y resultados del modelo
    return start, var_pred, model_fit.params, model_fit.loglikelihood, model_fit.aic, model_fit.bic

# Función para realizar el ajuste de GARCH para una variable
def procesar_variable(variable):
    predicciones = {}
    resultados_modelo = {}
    
    # Tomar la serie de entrenamiento para cada variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    for ventana in ventanas:
        predicciones[ventana] = {}
        resultados_modelo[ventana] = {}

        # Ejecutar rolling con paso fijo
        with ThreadPoolExecutor() as executor:
            futures = []
            for start in range(0, len(train_series) - ventana, step_size):  # Usamos step_size para saltar puntos
                futures.append(executor.submit(ajustar_garch, variable, ventana, start, train_series))
            
            # Obtener resultados de tareas paralelas
            for future in futures:
                start, var_pred, params, loglikelihood, aic, bic = future.result()
                
                # Guardar predicciones
                predicciones[ventana][start] = var_pred
                
                # Almacenar los resultados del modelo (parámetros ajustados, AIC, BIC)
                resultados_modelo[ventana][start] = {
                    'params': params,
                    'loglikelihood': loglikelihood,
                    'aic': aic,
                    'bic': bic
                }

    return predicciones, resultados_modelo

# Procesar cada variable por separado
print("Procesando variable: Price")
predicciones_price, resultados_modelo_price = procesar_variable('Price')

print("Procesando variable: Volatilidad_14")
predicciones_volatilidad, resultados_modelo_volatilidad = procesar_variable('Volatilidad_14')

print("Procesando variable: At")
predicciones_at, resultados_modelo_at = procesar_variable('At')

# Imprimir o almacenar resultados finales por variable
print("Predicciones Price:", predicciones_price)
print("Resultados Modelo Price:", resultados_modelo_price)

print("Predicciones Volatilidad_14:", predicciones_volatilidad)
print("Resultados Modelo Volatilidad_14:", resultados_modelo_volatilidad)

print("Predicciones At:", predicciones_at)
print("Resultados Modelo At:", resultados_modelo_at)

Procesando variable: Price

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

Procesando variable: Volatilidad_14

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

Procesando variable: At

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 8. The message is:
Positive directional derivative for linesearch
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

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Resultados Modelo Price: {14: {0: {'params': mu          6.780210e+04
omega       3.232496e+06
alpha[1]    2.083486e-15
alpha[2]    0.000000e+00
alpha[3]    6.252800e-01
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     2.779790e-01
Name: params, dtype: float64, 'loglikelihood': -132.83199230653787, 'aic': 287.66398461307574, 'bic': np.float64(294.69361523884356)}, 20: {'params': mu          5.717594e+04
omega       1.605338e+07
alpha[1]    4.863131e-01
alpha[2]    3.789135e-15
alpha[3]    2.455753e-14
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     3.659561e-02
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -140.67020365215893, 'aic': 303.34040730431786, 'bic': np.float64(310.3700379300857)}, 40: {'params': mu          4.519157e+04
omega       3.611449e+06
alpha[1]    5.210664e-01
alpha[2]    2.313208e-13
alpha[3]    2.552113e-13
beta[1]     2.148654e-13
beta[2]     2.388112e-13
beta[3]     2.726487e-13
beta[4]     3.009456e-13
beta[5]     2.509928e-13
beta[6]     2.037946e-13
Name: params, dtype: float64, 'loglikelihood': -129.3968844219655, 'aic': 280.793768843931, 'bic': np.float64(287.8233994696988)}, 60: {'params': mu          4.199688e+04
omega       8.044484e+05
alpha[1]    5.119276e-01
alpha[2]    6.613436e-11
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     1.109116e-01
beta[5]     0.000000e+00
beta[6]     3.771609e-01
Name: params, dtype: float64, 'loglikelihood': -123.22413994733682, 'aic': 268.44827989467365, 'bic': np.float64(275.47791052044147)}, 80: {'params': mu          4.324157e+04
omega       3.661451e+05
alpha[1]    2.862175e-02
alpha[2]    1.953705e-01
alpha[3]    2.425897e-01
beta[1]     1.452494e-15
beta[2]     2.145836e-15
beta[3]     3.864109e-15
beta[4]     1.452048e-15
beta[5]     2.399628e-15
beta[6]     3.487420e-15
Name: params, dtype: float64, 'loglikelihood': -113.98733026938477, 'aic': 249.97466053876954, 'bic': np.float64(257.0042911645374)}, 100: {'params': mu          4.248757e+04
omega       1.068956e+06
alpha[1]    4.145309e-01
alpha[2]    3.065399e-01
alpha[3]    0.000000e+00
beta[1]     1.370914e-16
beta[2]     3.833764e-16
beta[3]     1.844722e-16
beta[4]     0.000000e+00
beta[5]     1.750016e-16
beta[6]     2.896211e-16
Name: params, dtype: float64, 'loglikelihood': -121.12101926278238, 'aic': 264.2420385255648, 'bic': np.float64(271.2716691513326)}, 120: {'params': mu          3.693729e+04
omega       2.597291e+05
alpha[1]    3.027503e-01
alpha[2]    4.205751e-15
alpha[3]    2.425887e-15
beta[1]     6.464289e-15
beta[2]     5.235651e-15
beta[3]     4.571697e-15
beta[4]     6.689567e-02
beta[5]     3.825546e-15
beta[6]     1.405261e-01
Name: params, dtype: float64, 'loglikelihood': -111.83008710488059, 'aic': 245.66017420976118, 'bic': np.float64(252.68980483552903)}, 140: {'params': mu          3.445772e+04
omega       1.027357e+05
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    1.937997e-17
beta[1]     5.881684e-14
beta[2]     1.504668e-13
beta[3]     2.579340e-01
beta[4]     3.035577e-01
beta[5]     1.764064e-13
beta[6]     2.168997e-01
Name: params, dtype: float64, 'loglikelihood': -108.97427508935245, 'aic': 239.9485501787049, 'bic': np.float64(246.97818080447274)}, 160: {'params': mu          2.746058e+04
omega       1.274842e+05
alpha[1]    3.230829e-01
alpha[2]    8.531070e-02
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     7.720497e-02
beta[4]     1.240023e-15
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -106.67681537236878, 'aic': 235.35363074473756, 'bic': np.float64(242.3832613705054)}, 180: {'params': mu          2.657438e+04
omega       4.197571e+04
alpha[1]    4.379662e-01
alpha[2]    2.233113e-13
alpha[3]    4.598151e-13
beta[1]     3.056573e-13
beta[2]     4.244088e-13
beta[3]     3.111584e-13
beta[4]     3.203640e-13
beta[5]     1.247540e-13
beta[6]     1.884344e-01
Name: params, dtype: float64, 'loglikelihood': -98.26105914427994, 'aic': 218.52211828855988, 'bic': np.float64(225.55174891432773)}, 200: {'params': mu          2.617467e+04
omega       1.601688e+05
alpha[1]    5.893809e-01
alpha[2]    5.437818e-15
alpha[3]    3.167461e-14
beta[1]     7.837074e-14
beta[2]     8.331479e-14
beta[3]     8.491192e-14
beta[4]     8.233720e-14
beta[5]     6.148730e-14
beta[6]     5.407140e-14
Name: params, dtype: float64, 'loglikelihood': -106.68444547027222, 'aic': 235.36889094054445, 'bic': np.float64(242.3985215663123)}, 220: {'params': mu          2.909978e+04
omega       2.642971e+05
alpha[1]    1.000000e+00
alpha[2]    7.913870e-14
alpha[3]    5.887689e-14
beta[1]     1.124094e-14
beta[2]     0.000000e+00
beta[3]     3.086759e-14
beta[4]     7.228223e-15
beta[5]     1.512028e-14
beta[6]     1.940280e-14
Name: params, dtype: float64, 'loglikelihood': -108.94285088629326, 'aic': 239.88570177258651, 'bic': np.float64(246.91533239835437)}, 240: {'params': mu          2.985760e+04
omega       7.436812e+04
alpha[1]    7.084371e-01
alpha[2]    2.297837e-12
alpha[3]    2.470618e-12
beta[1]     2.027712e-12
beta[2]     2.316064e-12
beta[3]     2.499700e-12
beta[4]     2.750682e-12
beta[5]     2.815746e-12
beta[6]     2.539682e-12
Name: params, dtype: float64, 'loglikelihood': -101.55487753708032, 'aic': 225.10975507416063, 'bic': np.float64(232.13938569992848)}, 260: {'params': mu          3.047171e+04
omega       4.256206e+04
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    3.932985e-01
beta[1]     0.000000e+00
beta[2]     1.019716e-01
beta[3]     6.475150e-15
beta[4]     0.000000e+00
beta[5]     5.437334e-15
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -98.44788239555025, 'aic': 218.8957647911005, 'bic': np.float64(225.92539541686835)}, 280: {'params': mu          2.613042e+04
omega       1.215087e+05
alpha[1]    0.000000e+00
alpha[2]    4.062631e-10
alpha[3]    8.585965e-10
beta[1]     1.197760e-08
beta[2]     4.981875e-08
beta[3]     1.458846e-06
beta[4]     5.653262e-01
beta[5]     8.941182e-09
beta[6]     4.056899e-08
Name: params, dtype: float64, 'loglikelihood': -106.61355294105017, 'aic': 235.22710588210035, 'bic': np.float64(242.2567365078682)}, 300: {'params': mu           27019.071609
omega       102627.254849
alpha[1]         0.584947
alpha[2]         0.000000
alpha[3]         0.020452
beta[1]          0.000000
beta[2]          0.000000
beta[3]          0.000000
beta[4]          0.000000
beta[5]          0.000000
beta[6]          0.000000
Name: params, dtype: float64, 'loglikelihood': -103.98431551398492, 'aic': 229.96863102796985, 'bic': np.float64(236.9982616537377)}, 320: {'params': mu           28744.413253
omega       182009.322726
alpha[1]         0.282136
alpha[2]         0.000000
alpha[3]         0.000000
beta[1]          0.000000
beta[2]          0.000000
beta[3]          0.194488
beta[4]          0.000000
beta[5]          0.000000
beta[6]          0.000000
Name: params, dtype: float64, 'loglikelihood': -109.09258069620321, 'aic': 240.18516139240643, 'bic': np.float64(247.21479201817428)}, 340: {'params': mu           29432.352198
omega       477360.590120
alpha[1]         0.345701
alpha[2]         0.000000
alpha[3]         0.000000
beta[1]          0.000000
beta[2]          0.000000
beta[3]          0.000000
beta[4]          0.000000
beta[5]          0.000000
beta[6]          0.199976
Name: params, dtype: float64, 'loglikelihood': -115.8092604714596, 'aic': 253.6185209429192, 'bic': np.float64(260.648151568687)}, 360: {'params': mu          2.766822e+04
omega       9.756272e+04
alpha[1]    6.508522e-16
alpha[2]    0.000000e+00
alpha[3]    2.744547e-16
beta[1]     0.000000e+00
beta[2]     1.419573e-01
beta[3]     1.258095e-01
beta[4]     1.488447e-01
beta[5]     6.559745e-02
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -105.1299203480796, 'aic': 232.2598406961592, 'bic': np.float64(239.28947132192704)}, 380: {'params': mu          2.245887e+04
omega       5.713623e+05
alpha[1]    6.240647e-01
alpha[2]    3.964466e-10
alpha[3]    4.159980e-10
beta[1]     3.135001e-10
beta[2]     3.345146e-10
beta[3]     3.535246e-10
beta[4]     3.601733e-10
beta[5]     3.591463e-10
beta[6]     3.232735e-10
Name: params, dtype: float64, 'loglikelihood': -115.58575849745408, 'aic': 253.17151699490816, 'bic': np.float64(260.201147620676)}, 400: {'params': mu          2.285940e+04
omega       5.458097e+05
alpha[1]    3.129850e-01
alpha[2]    2.013745e-01
alpha[3]    0.000000e+00
beta[1]     4.347988e-17
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -116.34220398086461, 'aic': 254.68440796172922, 'bic': np.float64(261.71403858749704)}, 420: {'params': mu           22407.774037
omega       425845.208383
alpha[1]         0.531547
alpha[2]         0.000000
alpha[3]         0.000000
beta[1]          0.000000
beta[2]          0.000000
beta[3]          0.000000
beta[4]          0.000000
beta[5]          0.000000
beta[6]          0.000000
Name: params, dtype: float64, 'loglikelihood': -114.39196521003089, 'aic': 250.78393042006178, 'bic': np.float64(257.8135610458296)}, 440: {'params': mu          1.669784e+04
omega       1.987307e+04
alpha[1]    6.196971e-01
alpha[2]    3.704602e-13
alpha[3]    3.894591e-13
beta[1]     3.375721e-13
beta[2]     3.578157e-13
beta[3]     4.687782e-13
beta[4]     4.949784e-13
beta[5]     4.970249e-13
beta[6]     4.913699e-13
Name: params, dtype: float64, 'loglikelihood': -92.69625254579871, 'aic': 207.39250509159743, 'bic': np.float64(214.42213571736528)}, 460: {'params': mu          1.707430e+04
omega       7.244653e+04
alpha[1]    2.772397e-01
alpha[2]    3.448668e-01
alpha[3]    3.188366e-10
beta[1]     6.502678e-08
beta[2]     3.668353e-09
beta[3]     3.840474e-09
beta[4]     3.490836e-09
beta[5]     3.706214e-09
beta[6]     3.398659e-09
Name: params, dtype: float64, 'loglikelihood': -102.52599314657293, 'aic': 227.05198629314586, 'bic': np.float64(234.0816169189137)}, 480: {'params': mu          16481.424482
omega       46533.926717
alpha[1]        0.000000
alpha[2]        0.000000
alpha[3]        0.000000
beta[1]         0.430777
beta[2]         0.000000
beta[3]         0.000000
beta[4]         0.000000
beta[5]         0.000000
beta[6]         0.000000
Name: params, dtype: float64, 'loglikelihood': -99.83967870734683, 'aic': 221.67935741469367, 'bic': np.float64(228.70898804046152)}, 500: {'params': mu          1.995197e+04
omega       1.107425e+06
alpha[1]    6.516178e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -119.4408844583542, 'aic': 260.88176891670844, 'bic': np.float64(267.91139954247626)}, 520: {'params': mu          1.924570e+04
omega       1.199008e+04
alpha[1]    0.000000e+00
alpha[2]    5.848401e-01
alpha[3]    0.000000e+00
beta[1]     3.583008e-14
beta[2]     8.676801e-14
beta[3]     3.422197e-14
beta[4]     3.651432e-02
beta[5]     4.651283e-14
beta[6]     3.577777e-13
Name: params, dtype: float64, 'loglikelihood': -90.27989850953165, 'aic': 202.5597970190633, 'bic': np.float64(209.58942764483115)}, 540: {'params': mu          1.919934e+04
omega       4.767603e+04
alpha[1]    0.000000e+00
alpha[2]    7.829501e-14
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     2.306633e-01
beta[5]     0.000000e+00
beta[6]     3.537494e-01
Name: params, dtype: float64, 'loglikelihood': -100.03725514154756, 'aic': 222.07451028309512, 'bic': np.float64(229.10414090886297)}, 560: {'params': mu           20147.918537
omega       368743.644046
alpha[1]         0.653740
alpha[2]         0.000000
alpha[3]         0.000000
beta[1]          0.000000
beta[2]          0.000000
beta[3]          0.000000
beta[4]          0.000000
beta[5]          0.000000
beta[6]          0.000000
Name: params, dtype: float64, 'loglikelihood': -111.92173813563555, 'aic': 245.8434762712711, 'bic': np.float64(252.87310689703895)}, 580: {'params': mu          2.311378e+04
omega       7.983588e+05
alpha[1]    5.348078e-01
alpha[2]    3.947186e-11
alpha[3]    3.904151e-11
beta[1]     3.019569e-11
beta[2]     3.083640e-11
beta[3]     3.018616e-11
beta[4]     2.975538e-11
beta[5]     2.842692e-11
beta[6]     2.778532e-11
Name: params, dtype: float64, 'loglikelihood': -118.7979012518532, 'aic': 259.5958025037064, 'bic': np.float64(266.62543312947423)}, 600: {'params': mu           22886.912856
omega       296579.777452
alpha[1]         0.298338
alpha[2]         0.284358
alpha[3]         0.000000
beta[1]          0.000000
beta[2]          0.000000
beta[3]          0.000000
beta[4]          0.000000
beta[5]          0.000000
beta[6]          0.000000
Name: params, dtype: float64, 'loglikelihood': -112.39300086687284, 'aic': 246.78600173374568, 'bic': np.float64(253.81563235951353)}, 620: {'params': mu          2.028200e+04
omega       3.540745e+05
alpha[1]    2.851633e-01
alpha[2]    2.062809e-15
alpha[3]    1.819348e-15
beta[1]     1.956976e-15
beta[2]     1.451274e-15
beta[3]     1.010099e-15
beta[4]     0.000000e+00
beta[5]     2.090974e-01
beta[6]     2.055509e-16
Name: params, dtype: float64, 'loglikelihood': -113.78714857593188, 'aic': 249.57429715186376, 'bic': np.float64(256.6039277776316)}, 640: {'params': mu          2.243073e+04
omega       4.825247e+06
alpha[1]    5.735936e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     3.756160e-02
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -130.5358059158111, 'aic': 283.0716118316222, 'bic': np.float64(290.10124245739)}, 660: {'params': mu          2.984088e+04
omega       4.125403e+05
alpha[1]    1.706865e-01
alpha[2]    0.000000e+00
alpha[3]    2.402249e-13
beta[1]     2.853265e-13
beta[2]     3.452073e-13
beta[3]     3.085295e-01
beta[4]     2.628480e-13
beta[5]     3.527021e-13
beta[6]     2.329191e-11
Name: params, dtype: float64, 'loglikelihood': -114.92118741906259, 'aic': 251.84237483812518, 'bic': np.float64(258.872005463893)}, 680: {'params': mu          3.392668e+04
omega       7.514729e+06
alpha[1]    5.534359e-01
alpha[2]    2.732335e-13
alpha[3]    1.137678e-13
beta[1]     6.862750e-14
beta[2]     9.302234e-14
beta[3]     1.204904e-13
beta[4]     9.878618e-14
beta[5]     1.163868e-13
beta[6]     5.991765e-14
Name: params, dtype: float64, 'loglikelihood': -135.27176920287985, 'aic': 292.5435384057597, 'bic': np.float64(299.5731690315275)}, 700: {'params': mu          4.028828e+04
omega       2.374770e+05
alpha[1]    1.449744e-01
alpha[2]    0.000000e+00
alpha[3]    1.968977e-16
beta[1]     1.217752e-15
beta[2]     7.810360e-16
beta[3]     3.875570e-15
beta[4]     6.917979e-16
beta[5]     3.172891e-01
beta[6]     9.020562e-16
Name: params, dtype: float64, 'loglikelihood': -111.25010870219748, 'aic': 244.50021740439496, 'bic': np.float64(251.5298480301628)}, 720: {'params': mu          4.552387e+04
omega       1.231568e+06
alpha[1]    6.162164e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -121.5474006853396, 'aic': 265.0948013706792, 'bic': np.float64(272.124431996447)}, 740: {'params': mu           39694.697920
omega       895083.321369
alpha[1]         0.466128
alpha[2]         0.000000
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beta[1]          0.000000
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beta[3]          0.447373
beta[4]          0.000000
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Name: params, dtype: float64, 'loglikelihood': -123.10829679687232, 'aic': 268.2165935937446, 'bic': np.float64(275.2462242195125)}, 760: {'params': mu          4.090305e+04
omega       2.882837e+06
alpha[1]    4.230476e-01
alpha[2]    0.000000e+00
alpha[3]    2.239603e-15
beta[1]     0.000000e+00
beta[2]     1.785999e-15
beta[3]     4.507948e-16
beta[4]     9.475842e-02
beta[5]     0.000000e+00
beta[6]     0.000000e+00
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omega       1.971978e+05
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Name: params, dtype: float64, 'loglikelihood': -109.2453434878171, 'aic': 240.4906869756342, 'bic': np.float64(247.52031760140204)}, 1600: {'params': mu          9.290573e+03
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Name: params, dtype: float64, 'loglikelihood': -100.90909354833322, 'aic': 223.81818709666643, 'bic': np.float64(230.84781772243429)}, 1620: {'params': mu           8222.565022
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Name: params, dtype: float64, 'loglikelihood': -92.677520269053, 'aic': 207.355040538106, 'bic': np.float64(214.38467116387386)}, 1640: {'params': mu            9615.014838
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Name: params, dtype: float64, 'loglikelihood': -112.90781552684457, 'aic': 247.81563105368915, 'bic': np.float64(254.845261679457)}, 1660: {'params': mu          1.012065e+04
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Name: params, dtype: float64, 'loglikelihood': -103.1951081691846, 'aic': 228.3902163383692, 'bic': np.float64(235.41984696413707)}, 1680: {'params': mu          1.113794e+04
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Name: params, dtype: float64, 'loglikelihood': -112.16177923959437, 'aic': 246.32355847918873, 'bic': np.float64(253.35318910495658)}, 1700: {'params': mu          1.004245e+04
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Name: params, dtype: float64, 'loglikelihood': -105.52587830668043, 'aic': 233.05175661336085, 'bic': np.float64(240.0813872391287)}, 1720: {'params': mu           11603.598595
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Name: params, dtype: float64, 'loglikelihood': -111.88033899079389, 'aic': 245.76067798158778, 'bic': np.float64(252.79030860735563)}, 1740: {'params': mu            8401.426630
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Name: params, dtype: float64, 'loglikelihood': -108.2089049995117, 'aic': 238.4178099990234, 'bic': np.float64(245.44744062479126)}, 1760: {'params': mu          8.084742e+03
omega       1.079291e+05
alpha[1]    2.958811e-01
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Name: params, dtype: float64, 'loglikelihood': -105.51576767517744, 'aic': 233.0315353503549, 'bic': np.float64(240.06116597612274)}, 1780: {'params': mu           5681.245006
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Name: params, dtype: float64, 'loglikelihood': -100.28824419999235, 'aic': 222.5764883999847, 'bic': np.float64(229.60611902575255)}, 1800: {'params': mu          5.168974e+03
omega       4.433136e+03
alpha[1]    9.232255e-16
alpha[2]    1.847583e-01
alpha[3]    0.000000e+00
beta[1]     1.044319e-14
beta[2]     8.554328e-15
beta[3]     1.253125e-01
beta[4]     1.249356e-14
beta[5]     1.973450e-01
beta[6]     8.008411e-15
Name: params, dtype: float64, 'loglikelihood': -83.42589304418203, 'aic': 188.85178608836407, 'bic': np.float64(195.88141671413192)}, 1820: {'params': mu          4.006650e+03
omega       1.425089e+03
alpha[1]    6.071717e-01
alpha[2]    0.000000e+00
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beta[3]     1.502719e-13
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Name: params, dtype: float64, 'loglikelihood': -73.75800002481205, 'aic': 169.5160000496241, 'bic': np.float64(176.54563067539195)}, 1840: {'params': mu          3.840631e+03
omega       8.371157e+02
alpha[1]    2.135497e-12
alpha[2]    0.000000e+00
alpha[3]    3.343076e-12
beta[1]     1.957499e-11
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beta[3]     4.036331e-01
beta[4]     9.589598e-10
beta[5]     1.951168e-01
beta[6]     1.148322e-10
Name: params, dtype: float64, 'loglikelihood': -75.23974283612563, 'aic': 172.47948567225126, 'bic': np.float64(179.5091162980191)}, 1860: {'params': mu          3618.673790
omega       9394.401174
alpha[1]       0.986863
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Name: params, dtype: float64, 'loglikelihood': -86.03151239583231, 'aic': 194.06302479166462, 'bic': np.float64(201.09265541743247)}, 1880: {'params': mu          3573.343089
omega       2354.236228
alpha[1]       0.760205
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Name: params, dtype: float64, 'loglikelihood': -77.05244829725812, 'aic': 176.10489659451625, 'bic': np.float64(183.1345272202841)}, 1900: {'params': mu          3.815716e+03
omega       6.635822e+03
alpha[1]    1.367924e-13
alpha[2]    6.443300e-01
alpha[3]    1.082825e-13
beta[1]     1.056795e-13
beta[2]     8.131577e-14
beta[3]     1.870636e-13
beta[4]     7.926433e-14
beta[5]     1.662218e-13
beta[6]     1.688769e-13
Name: params, dtype: float64, 'loglikelihood': -84.97070583555055, 'aic': 191.9414116711011, 'bic': np.float64(198.97104229686894)}, 1920: {'params': mu          3.446292e+03
omega       2.757161e+04
alpha[1]    6.356108e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
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beta[3]     6.577002e-13
beta[4]     0.000000e+00
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beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -94.1589494745844, 'aic': 210.3178989491688, 'bic': np.float64(217.34752957493666)}, 1940: {'params': mu          4.138860e+03
omega       6.443391e+04
alpha[1]    1.000000e+00
alpha[2]    0.000000e+00
alpha[3]    1.689437e-14
beta[1]     2.136728e-13
beta[2]     1.590692e-13
beta[3]     2.817852e-13
beta[4]     9.765742e-14
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -102.17742680077558, 'aic': 226.35485360155116, 'bic': np.float64(233.384484227319)}, 1960: {'params': mu          6.425017e+03
omega       2.005178e+03
alpha[1]    7.371298e-01
alpha[2]    6.888402e-15
alpha[3]    7.524399e-15
beta[1]     2.966715e-14
beta[2]     2.910210e-14
beta[3]     2.821707e-14
beta[4]     2.691128e-14
beta[5]     2.546192e-14
beta[6]     2.207577e-02
Name: params, dtype: float64, 'loglikelihood': -77.19708402757504, 'aic': 176.3941680551501, 'bic': np.float64(183.42379868091794)}, 1980: {'params': mu           6563.142940
omega       12132.994944
alpha[1]        0.655553
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Name: params, dtype: float64, 'loglikelihood': -88.61862206392932, 'aic': 199.23724412785865, 'bic': np.float64(206.2668747536265)}, 2000: {'params': mu          6.614464e+03
omega       5.915506e+03
alpha[1]    8.581137e-01
alpha[2]    2.267499e-14
alpha[3]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -84.21481265822786, 'aic': 190.4296253164557, 'bic': np.float64(197.45925594222356)}, 2020: {'params': mu          6.724284e+03
omega       9.313891e+04
alpha[1]    1.587344e-01
alpha[2]    0.000000e+00
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beta[5]     3.341464e-01
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Name: params, dtype: float64, 'loglikelihood': -104.73420617616324, 'aic': 231.46841235232648, 'bic': np.float64(238.49804297809433)}, 2040: {'params': mu          6.341386e+03
omega       3.198437e+02
alpha[1]    1.524813e-15
alpha[2]    1.814260e-16
alpha[3]    4.686324e-16
beta[1]     1.627162e-01
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beta[4]     1.639655e-01
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Name: params, dtype: float64, 'loglikelihood': -87.62420748770467, 'aic': 197.24841497540933, 'bic': np.float64(204.27804560117718)}, 2060: {'params': mu          7.869018e+03
omega       3.601100e+04
alpha[1]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -101.65971850970399, 'aic': 225.31943701940799, 'bic': np.float64(232.34906764517584)}, 2080: {'params': mu          6.524403e+03
omega       1.590174e+04
alpha[1]    5.799617e-01
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Name: params, dtype: float64, 'loglikelihood': -91.59494507432909, 'aic': 205.18989014865818, 'bic': np.float64(212.21952077442603)}, 2100: {'params': mu          6.544849e+03
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alpha[1]    1.459644e-14
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Name: params, dtype: float64, 'loglikelihood': -96.14948794226808, 'aic': 214.29897588453616, 'bic': np.float64(221.328606510304)}, 2120: {'params': mu          7.515541e+03
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alpha[1]    0.000000e+00
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beta[6]     8.018424e-01
Name: params, dtype: float64, 'loglikelihood': -93.28228041998074, 'aic': 208.56456083996147, 'bic': np.float64(215.59419146572932)}, 2140: {'params': mu            9135.479423
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Name: params, dtype: float64, 'loglikelihood': -106.36177440572989, 'aic': 234.72354881145978, 'bic': np.float64(241.75317943722763)}, 2160: {'params': mu          8.478403e+03
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alpha[1]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -107.14985665561147, 'aic': 236.29971331122294, 'bic': np.float64(243.3293439369908)}, 2180: {'params': mu            7547.646905
omega       258681.001140
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Name: params, dtype: float64, 'loglikelihood': -111.11442597014785, 'aic': 244.2288519402957, 'bic': np.float64(251.25848256606355)}, 2200: {'params': mu            9613.726739
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Name: params, dtype: float64, 'loglikelihood': -116.59000766124842, 'aic': 255.18001532249684, 'bic': np.float64(262.20964594826467)}, 2220: {'params': mu          9.949076e+03
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Name: params, dtype: float64, 'loglikelihood': -114.56746282837078, 'aic': 251.13492565674156, 'bic': np.float64(258.1645562825094)}, 2240: {'params': mu           10429.855489
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Name: params, dtype: float64, 'loglikelihood': -117.12677057203139, 'aic': 256.25354114406275, 'bic': np.float64(263.28317176983063)}, 2260: {'params': mu           14953.620853
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Name: params, dtype: float64, 'loglikelihood': -116.99454292921526, 'aic': 255.9890858584305, 'bic': np.float64(263.01871648419836)}, 2280: {'params': mu          1.634303e+04
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Name: params, dtype: float64, 'loglikelihood': -124.92857758789692, 'aic': 271.8571551757939, 'bic': np.float64(278.8867858015617)}, 2300: {'params': mu          1.026944e+04
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alpha[1]    8.269484e-01
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Name: params, dtype: float64, 'loglikelihood': -120.35917335660372, 'aic': 262.71834671320744, 'bic': np.float64(269.74797733897526)}, 2320: {'params': mu          6.970131e+03
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Name: params, dtype: float64, 'loglikelihood': -106.6535632635177, 'aic': 235.3071265270354, 'bic': np.float64(242.33675715280324)}, 2340: {'params': mu          5.780729e+03
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alpha[1]    2.499898e-14
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Name: params, dtype: float64, 'loglikelihood': -90.32153285386438, 'aic': 202.64306570772877, 'bic': np.float64(209.67269633349662)}, 2360: {'params': mu          4.304381e+03
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alpha[1]    5.949432e-01
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Name: params, dtype: float64, 'loglikelihood': -92.97239967751466, 'aic': 207.94479935502932, 'bic': np.float64(214.97442998079717)}, 2380: {'params': mu          4.102214e+03
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beta[4]     4.165985e-01
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Name: params, dtype: float64, 'loglikelihood': -206.85013993803105, 'aic': 435.7002798760621, 'bic': np.float64(450.35452948798934)}, 1680: {'params': mu           10604.484861
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Name: params, dtype: float64, 'loglikelihood': -224.90458927305087, 'aic': 471.80917854610175, 'bic': np.float64(486.463428158029)}, 1700: {'params': mu           10734.573395
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Name: params, dtype: float64, 'loglikelihood': -228.0533219427407, 'aic': 478.1066438854814, 'bic': np.float64(492.76089349740863)}, 1720: {'params': mu           10609.307780
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Name: params, dtype: float64, 'loglikelihood': -239.6330396411039, 'aic': 501.2660792822078, 'bic': np.float64(515.9203288941351)}, 1740: {'params': mu          8.354217e+03
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Name: params, dtype: float64, 'loglikelihood': -210.93084495788685, 'aic': 443.8616899157737, 'bic': np.float64(458.51593952770094)}, 1760: {'params': mu            7788.396469
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Name: params, dtype: float64, 'loglikelihood': -228.06687690680542, 'aic': 478.13375381361084, 'bic': np.float64(492.7880034255381)}, 1780: {'params': mu           5322.251897
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Name: params, dtype: float64, 'loglikelihood': -196.4663143152167, 'aic': 414.9326286304334, 'bic': np.float64(429.5868782423606)}, 1800: {'params': mu          5.104322e+03
omega       7.854691e+04
alpha[1]    9.472893e-01
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Name: params, dtype: float64, 'loglikelihood': -205.48294207105891, 'aic': 432.96588414211783, 'bic': np.float64(447.62013375404507)}, 1820: {'params': mu          3975.456107
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Name: params, dtype: float64, 'loglikelihood': -161.99700283855728, 'aic': 345.99400567711456, 'bic': np.float64(360.6482552890418)}, 1840: {'params': mu          3.846871e+03
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alpha[1]    8.133746e-01
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beta[5]     8.272388e-02
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Name: params, dtype: float64, 'loglikelihood': -170.39308135738125, 'aic': 362.7861627147625, 'bic': np.float64(377.44041232668974)}, 1860: {'params': mu          3568.416827
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Name: params, dtype: float64, 'loglikelihood': -170.7285914990357, 'aic': 363.4571829980714, 'bic': np.float64(378.11143260999864)}, 1880: {'params': mu           3600.265983
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Name: params, dtype: float64, 'loglikelihood': -177.35081898111372, 'aic': 376.70163796222744, 'bic': np.float64(391.3558875741547)}, 1900: {'params': mu          3.811054e+03
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alpha[1]    6.632207e-01
alpha[2]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -184.77966730227988, 'aic': 391.55933460455975, 'bic': np.float64(406.213584216487)}, 1920: {'params': mu          3.727966e+03
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alpha[1]    4.071186e-01
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beta[6]     6.176414e-02
Name: params, dtype: float64, 'loglikelihood': -200.84567684255538, 'aic': 423.69135368511076, 'bic': np.float64(438.345603297038)}, 1940: {'params': mu            5299.719242
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alpha[1]         0.545620
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Name: params, dtype: float64, 'loglikelihood': -232.50391378279517, 'aic': 487.00782756559033, 'bic': np.float64(501.6620771775176)}, 1960: {'params': mu          6498.102427
omega       4766.173780
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Name: params, dtype: float64, 'loglikelihood': -163.67178159840273, 'aic': 349.34356319680546, 'bic': np.float64(363.9978128087327)}, 1980: {'params': mu          6586.448649
omega       7805.194564
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Name: params, dtype: float64, 'loglikelihood': -168.4536486072891, 'aic': 358.9072972145782, 'bic': np.float64(373.56154682650543)}, 2000: {'params': mu          6.526436e+03
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alpha[1]    6.413141e-01
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Name: params, dtype: float64, 'loglikelihood': -179.90271073208922, 'aic': 381.80542146417844, 'bic': np.float64(396.4596710761057)}, 2020: {'params': mu           6476.924761
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Name: params, dtype: float64, 'loglikelihood': -212.742049153953, 'aic': 447.484098307906, 'bic': np.float64(462.1383479198332)}, 2060: {'params': mu          7.298635e+03
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Name: params, dtype: float64, 'loglikelihood': -220.00071737185053, 'aic': 462.00143474370105, 'bic': np.float64(476.6556843556283)}, 2080: {'params': mu          6.415537e+03
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Name: params, dtype: float64, 'loglikelihood': -193.45949946370322, 'aic': 408.91899892740645, 'bic': np.float64(423.5732485393337)}, 2100: {'params': mu          6.997387e+03
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Name: params, dtype: float64, 'loglikelihood': -215.31163306505928, 'aic': 452.62326613011857, 'bic': np.float64(467.2775157420458)}, 2120: {'params': mu          8.046484e+03
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Name: params, dtype: float64, 'loglikelihood': -216.67343455801014, 'aic': 455.3468691160203, 'bic': np.float64(470.0011187279475)}, 2140: {'params': mu            9062.533683
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Name: params, dtype: float64, 'loglikelihood': -209.23585954648615, 'aic': 440.4717190929723, 'bic': np.float64(455.12596870489955)}, 2160: {'params': mu            7703.089392
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Name: params, dtype: float64, 'loglikelihood': -230.1002235873164, 'aic': 482.2004471746328, 'bic': np.float64(496.85469678656005)}, 2220: {'params': mu            9498.348692
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Name: params, dtype: float64, 'loglikelihood': -236.7828964024956, 'aic': 495.5657928049912, 'bic': np.float64(510.22004241691843)}, 2280: {'params': mu          1.483092e+04
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Name: params, dtype: float64, 'loglikelihood': -155.0697135650492, 'aic': 332.1394271300984, 'bic': np.float64(343.62917394505604)}, 1540: {'params': mu           7215.936970
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Name: params, dtype: float64, 'loglikelihood': -165.3174487180181, 'aic': 352.6348974360362, 'bic': np.float64(364.12464425099387)}, 1600: {'params': mu            8736.413552
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Name: params, dtype: float64, 'loglikelihood': -161.67371924228448, 'aic': 345.34743848456895, 'bic': np.float64(356.8371852995266)}, 1660: {'params': mu          1.028581e+04
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Name: params, dtype: float64, 'loglikelihood': -152.9147425249242, 'aic': 327.8294850498484, 'bic': np.float64(339.31923186480606)}, 1680: {'params': mu           10848.795453
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Name: params, dtype: float64, 'loglikelihood': -159.599649992902, 'aic': 341.199299985804, 'bic': np.float64(352.6890468007616)}, 1760: {'params': mu          7.884990e+03
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Name: params, dtype: float64, 'loglikelihood': -161.25586306484738, 'aic': 344.51172612969475, 'bic': np.float64(356.0014729446524)}, 1780: {'params': mu          5.411795e+03
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Name: params, dtype: float64, 'loglikelihood': -148.62606179661563, 'aic': 319.25212359323126, 'bic': np.float64(330.7418704081889)}, 1800: {'params': mu          5.141487e+03
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alpha[1]    1.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -144.0163086891481, 'aic': 310.0326173782962, 'bic': np.float64(321.52236419325385)}, 1820: {'params': mu          3.992823e+03
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alpha[1]    6.801081e-01
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Name: params, dtype: float64, 'loglikelihood': -116.07800209342386, 'aic': 254.15600418684772, 'bic': np.float64(265.64575100180537)}, 1840: {'params': mu          3.862728e+03
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alpha[1]    4.818193e-01
alpha[2]    1.091465e-11
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Name: params, dtype: float64, 'loglikelihood': -121.86230922305798, 'aic': 265.724618446116, 'bic': np.float64(277.2143652610736)}, 1860: {'params': mu          3.582182e+03
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alpha[1]    6.297566e-01
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beta[4]     3.616840e-11
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Name: params, dtype: float64, 'loglikelihood': -130.6514344284687, 'aic': 283.3028688569374, 'bic': np.float64(294.792615671895)}, 1880: {'params': mu          3.580059e+03
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alpha[1]    6.381898e-01
alpha[2]    4.152742e-09
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Name: params, dtype: float64, 'loglikelihood': -113.78237152081968, 'aic': 249.56474304163936, 'bic': np.float64(261.054489856597)}, 1900: {'params': mu          3838.861259
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Name: params, dtype: float64, 'loglikelihood': -130.2411177805882, 'aic': 282.4822355611764, 'bic': np.float64(293.97198237613406)}, 1920: {'params': mu          3.496669e+03
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alpha[1]    8.020626e-01
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Name: params, dtype: float64, 'loglikelihood': -146.63979434307964, 'aic': 315.2795886861593, 'bic': np.float64(326.7693355011169)}, 1940: {'params': mu            4908.209376
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Name: params, dtype: float64, 'loglikelihood': -170.99299270113787, 'aic': 363.98598540227573, 'bic': np.float64(375.47573221723337)}, 1960: {'params': mu          6.457917e+03
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alpha[1]    3.487706e-01
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alpha[3]    8.802467e-14
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beta[4]     1.699873e-13
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beta[6]     3.812713e-01
Name: params, dtype: float64, 'loglikelihood': -117.30943399067381, 'aic': 256.61886798134765, 'bic': np.float64(268.1086147963053)}, 1980: {'params': mu          6.578995e+03
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alpha[1]    6.266997e-01
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alpha[3]    2.989735e-12
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beta[3]     3.480776e-12
beta[4]     4.308651e-12
beta[5]     4.147685e-12
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Name: params, dtype: float64, 'loglikelihood': -128.14897665889686, 'aic': 278.2979533177937, 'bic': np.float64(289.78770013275135)}, 2000: {'params': mu          6.534207e+03
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alpha[1]    5.350200e-01
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beta[4]     2.493049e-01
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Name: params, dtype: float64, 'loglikelihood': -131.60677300384742, 'aic': 285.21354600769484, 'bic': np.float64(296.7032928226525)}, 2020: {'params': mu          6.751956e+03
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alpha[1]    4.054374e-01
alpha[2]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -152.94972269715038, 'aic': 327.89944539430076, 'bic': np.float64(339.3891922092584)}, 2040: {'params': mu          6.394831e+03
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alpha[1]    8.749953e-01
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Name: params, dtype: float64, 'loglikelihood': -144.24246715697228, 'aic': 310.48493431394456, 'bic': np.float64(321.9746811289022)}, 2060: {'params': mu          7.573171e+03
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alpha[1]    7.030053e-01
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Name: params, dtype: float64, 'loglikelihood': -159.74401745764735, 'aic': 341.4880349152947, 'bic': np.float64(352.97778173025233)}, 2080: {'params': mu           6380.250267
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Name: params, dtype: float64, 'loglikelihood': -143.51830629658394, 'aic': 309.0366125931679, 'bic': np.float64(320.52635940812553)}, 2100: {'params': mu            6648.466699
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Name: params, dtype: float64, 'loglikelihood': -158.4731343795593, 'aic': 338.9462687591186, 'bic': np.float64(350.43601557407624)}, 2120: {'params': mu          7.570280e+03
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Name: params, dtype: float64, 'loglikelihood': -153.16560799934066, 'aic': 328.33121599868133, 'bic': np.float64(339.82096281363897)}, 2140: {'params': mu          9.146957e+03
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Name: params, dtype: float64, 'loglikelihood': -154.44799373549142, 'aic': 330.89598747098285, 'bic': np.float64(342.3857342859405)}, 2160: {'params': mu          7.935202e+03
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alpha[1]    6.374279e-01
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Name: params, dtype: float64, 'loglikelihood': -170.02757306682574, 'aic': 362.0551461336515, 'bic': np.float64(373.5448929486091)}, 2180: {'params': mu          7.866396e+03
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alpha[1]    5.410010e-01
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Name: params, dtype: float64, 'loglikelihood': -168.11730428591392, 'aic': 358.23460857182783, 'bic': np.float64(369.7243553867855)}, 2200: {'params': mu            9848.930867
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Name: params, dtype: float64, 'loglikelihood': -45.9688356972989, 'aic': 113.9376713945978, 'bic': np.float64(113.34268303420625)}, 1500: {'params': mu          1.014523e+04
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Name: params, dtype: float64, 'loglikelihood': -45.76986504749004, 'aic': 113.53973009498009, 'bic': np.float64(112.94474173458853)}, 1520: {'params': mu          8.563736e+03
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Name: params, dtype: float64, 'loglikelihood': -44.91946954202672, 'aic': 111.83893908405344, 'bic': np.float64(111.24395072366188)}, 1540: {'params': mu          7245.340790
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Name: params, dtype: float64, 'loglikelihood': -42.92703098557618, 'aic': 107.85406197115236, 'bic': np.float64(107.25907361076081)}, 1580: {'params': mu          7.360966e+03
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Name: params, dtype: float64, 'loglikelihood': -51.03525585451251, 'aic': 124.07051170902503, 'bic': np.float64(123.47552334863347)}, 1600: {'params': mu          9.275419e+03
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Name: params, dtype: float64, 'loglikelihood': -40.49067234081494, 'aic': 102.98134468162988, 'bic': np.float64(102.38635632123832)}, 1620: {'params': mu          8.206843e+03
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Name: params, dtype: float64, 'loglikelihood': -43.25867335014624, 'aic': 108.51734670029248, 'bic': np.float64(107.92235833990092)}, 1640: {'params': mu          8.988823e+03
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Name: params, dtype: float64, 'loglikelihood': -56.778564441851636, 'aic': 135.55712888370329, 'bic': np.float64(134.96214052331172)}, 1660: {'params': mu          1.037087e+04
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Name: params, dtype: float64, 'loglikelihood': -49.11878163903595, 'aic': 120.2375632780719, 'bic': np.float64(119.64257491768035)}, 1680: {'params': mu          10500.884196
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Name: params, dtype: float64, 'loglikelihood': -52.06195314271426, 'aic': 126.12390628542852, 'bic': np.float64(125.52891792503696)}, 1700: {'params': mu          9.752904e+03
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alpha[1]    2.487283e-14
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Name: params, dtype: float64, 'loglikelihood': -44.5856389810734, 'aic': 111.1712779621468, 'bic': np.float64(110.57628960175525)}, 1720: {'params': mu           11644.577230
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Name: params, dtype: float64, 'loglikelihood': -54.028965362394075, 'aic': 130.05793072478815, 'bic': np.float64(129.4629423643966)}, 1740: {'params': mu          8.900714e+03
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alpha[1]    3.855038e-14
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Name: params, dtype: float64, 'loglikelihood': -50.89539011306223, 'aic': 123.79078022612445, 'bic': np.float64(123.1957918657329)}, 1760: {'params': mu          8.431990e+03
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alpha[1]    3.083972e-01
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Name: params, dtype: float64, 'loglikelihood': -50.02294763884379, 'aic': 122.04589527768758, 'bic': np.float64(121.45090691729602)}, 1780: {'params': mu          5.966848e+03
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alpha[1]    3.807678e-01
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Name: params, dtype: float64, 'loglikelihood': -47.61047354097315, 'aic': 117.2209470819463, 'bic': np.float64(116.62595872155475)}, 1800: {'params': mu          5.185342e+03
omega       3.320306e+03
alpha[1]    2.955022e-13
alpha[2]    8.570172e-14
alpha[3]    5.456963e-01
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Name: params, dtype: float64, 'loglikelihood': -40.603373943000236, 'aic': 103.20674788600047, 'bic': np.float64(102.61175952560892)}, 1820: {'params': mu          4.037673e+03
omega       2.366649e+03
alpha[1]    2.847155e-01
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Name: params, dtype: float64, 'loglikelihood': -39.4443526398973, 'aic': 100.8887052797946, 'bic': np.float64(100.29371691940305)}, 1840: {'params': mu          3.884368e+03
omega       4.544264e+02
alpha[1]    2.175545e-15
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Name: params, dtype: float64, 'loglikelihood': -33.73882561512873, 'aic': 89.47765123025746, 'bic': np.float64(88.88266286986591)}, 1860: {'params': mu          3.637439e+03
omega       8.642326e+03
alpha[1]    8.935272e-01
alpha[2]    2.006114e-13
alpha[3]    7.808207e-14
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Name: params, dtype: float64, 'loglikelihood': -43.19676419768906, 'aic': 108.39352839537813, 'bic': np.float64(107.79854003498657)}, 1880: {'params': mu          3.512932e+03
omega       2.127578e+03
alpha[1]    0.000000e+00
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beta[1]     6.504845e-16
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beta[4]     3.434752e-16
beta[5]     2.085064e-16
beta[6]     1.035485e-15
Name: params, dtype: float64, 'loglikelihood': -39.1678352433227, 'aic': 100.3356704866454, 'bic': np.float64(99.74068212625384)}, 1900: {'params': mu          3.875834e+03
omega       9.688925e+03
alpha[1]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -44.36330453365385, 'aic': 110.7266090673077, 'bic': np.float64(110.13162070691615)}, 1920: {'params': mu          3.612110e+03
omega       4.057226e+04
alpha[1]    1.889689e-13
alpha[2]    1.448625e-14
alpha[3]    0.000000e+00
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beta[5]     5.810804e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -49.48045846219303, 'aic': 120.96091692438605, 'bic': np.float64(120.3659285639945)}, 1940: {'params': mu          4.080507e+03
omega       1.437988e+04
alpha[1]    1.603845e-15
alpha[2]    3.263898e-15
alpha[3]    0.000000e+00
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beta[3]     1.128264e-14
beta[4]     5.985670e-14
beta[5]     4.289553e-14
beta[6]     2.079359e-14
Name: params, dtype: float64, 'loglikelihood': -45.85139696808716, 'aic': 113.70279393617432, 'bic': np.float64(113.10780557578276)}, 1960: {'params': mu          6471.633077
omega       1146.664372
alpha[1]       0.000000
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Name: params, dtype: float64, 'loglikelihood': -36.59151183722494, 'aic': 95.18302367444988, 'bic': np.float64(94.58803531405833)}, 1980: {'params': mu          6.598423e+03
omega       2.142904e+03
alpha[1]    1.601674e-14
alpha[2]    1.157827e-01
alpha[3]    3.532299e-01
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beta[3]     1.031768e-14
beta[4]     1.058366e-14
beta[5]     2.295931e-01
beta[6]     1.422096e-14
Name: params, dtype: float64, 'loglikelihood': -39.05886805391784, 'aic': 100.11773610783568, 'bic': np.float64(99.52274774744413)}, 2000: {'params': mu          6608.018452
omega       2176.244940
alpha[1]       1.000000
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Name: params, dtype: float64, 'loglikelihood': -38.170777457392624, 'aic': 98.34155491478525, 'bic': np.float64(97.7465665543937)}, 2020: {'params': mu          6.325747e+03
omega       4.892163e+03
alpha[1]    3.489701e-16
alpha[2]    4.491532e-01
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beta[2]     9.333741e-17
beta[3]     2.875921e-01
beta[4]     3.709709e-15
beta[5]     1.030946e-16
beta[6]     2.919871e-16
Name: params, dtype: float64, 'loglikelihood': -41.74100524844399, 'aic': 105.48201049688798, 'bic': np.float64(104.88702213649643)}, 2040: {'params': mu          6.423283e+03
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alpha[1]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': -41.74626534617372, 'aic': 105.49253069234744, 'bic': np.float64(104.89754233195589)}, 2060: {'params': mu          7.845312e+03
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alpha[1]    3.092800e-01
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beta[6]     2.012279e-16
Name: params, dtype: float64, 'loglikelihood': -50.40665820383298, 'aic': 122.81331640766597, 'bic': np.float64(122.21832804727441)}, 2080: {'params': mu           6401.943932
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Name: params, dtype: float64, 'loglikelihood': -46.356357992325954, 'aic': 114.71271598465191, 'bic': np.float64(114.11772762426035)}, 2100: {'params': mu          6.477611e+03
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Name: params, dtype: float64, 'loglikelihood': -49.999447916981936, 'aic': 121.99889583396387, 'bic': np.float64(121.40390747357232)}, 2120: {'params': mu          7.540196e+03
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alpha[1]    2.444517e-16
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Name: params, dtype: float64, 'loglikelihood': -42.38129813045188, 'aic': 106.76259626090376, 'bic': np.float64(106.16760790051221)}, 2140: {'params': mu           8626.164297
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Name: params, dtype: float64, 'loglikelihood': -48.96345825161339, 'aic': 119.92691650322678, 'bic': np.float64(119.33192814283522)}, 2160: {'params': mu          8.908404e+03
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alpha[1]    1.855591e-10
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Name: params, dtype: float64, 'loglikelihood': -51.23412909091405, 'aic': 124.4682581818281, 'bic': np.float64(123.87326982143655)}, 2180: {'params': mu          6.957227e+03
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alpha[1]    3.700558e-14
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beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     1.217103e-02
beta[4]     3.052148e-02
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 0.6166744276907868, 'aic': 20.766651144618425, 'bic': np.float64(20.17166278422687)}, 4620: {'params': mu          1.360525e+01
omega       1.874002e-02
alpha[1]    9.245297e-01
alpha[2]    8.950285e-13
alpha[3]    6.360381e-14
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     7.547029e-02
beta[5]     8.468785e-11
beta[6]     3.804838e-11
Name: params, dtype: float64, 'loglikelihood': 0.016500539147457305, 'aic': 21.966998921705084, 'bic': np.float64(21.37201056131353)}, 4640: {'params': mu          1.433120e+01
omega       1.347273e-01
alpha[1]    0.000000e+00
alpha[2]    5.046708e-01
alpha[3]    0.000000e+00
beta[1]     3.759568e-11
beta[2]     1.701169e-11
beta[3]     9.687238e-11
beta[4]     2.255692e-10
beta[5]     7.977327e-10
beta[6]     4.953292e-01
Name: params, dtype: float64, 'loglikelihood': -6.407949486574278, 'aic': 34.815898973148556, 'bic': np.float64(34.220910612757)}, 4660: {'params': mu          1.695848e+01
omega       1.107065e-08
alpha[1]    0.000000e+00
alpha[2]    1.000000e+00
alpha[3]    1.512827e-12
beta[1]     1.533469e-12
beta[2]     2.703118e-13
beta[3]     7.360713e-12
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -7.747296674933979, 'aic': 37.494593349867955, 'bic': np.float64(36.8996049894764)}, 4680: {'params': mu          8.652013e+00
omega       2.075830e-09
alpha[1]    5.080910e-11
alpha[2]    4.073514e-11
alpha[3]    8.249686e-09
beta[1]     8.018579e-01
beta[2]     1.359729e-10
beta[3]     4.466685e-10
beta[4]     4.290431e-10
beta[5]     4.312610e-10
beta[6]     4.359909e-10
Name: params, dtype: float64, 'loglikelihood': -2.5976043480092357, 'aic': 27.195208696018472, 'bic': np.float64(26.60022033562692)}, 4700: {'params': mu          4.565402e+00
omega       1.210612e-08
alpha[1]    0.000000e+00
alpha[2]    1.104357e-01
alpha[3]    1.687008e-16
beta[1]     1.290455e-01
beta[2]     0.000000e+00
beta[3]     3.448326e-01
beta[4]     3.196959e-01
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -10.562680080450722, 'aic': 43.125360160901444, 'bic': np.float64(42.53037180050989)}, 4720: {'params': mu          1.162231e+00
omega       3.071252e-03
alpha[1]    1.949598e-13
alpha[2]    2.113188e-13
alpha[3]    2.292229e-13
beta[1]     6.541866e-01
beta[2]     0.000000e+00
beta[3]     2.336908e-12
beta[4]     4.004388e-12
beta[5]     2.141087e-12
beta[6]     2.271494e-12
Name: params, dtype: float64, 'loglikelihood': 5.285107150555259, 'aic': 11.429785698889482, 'bic': np.float64(10.834797338497928)}, 4740: {'params': mu          0.800000
omega       0.000000
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 4760: {'params': mu          9.000000e-01
omega       6.162976e-33
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 247.225034255307, 'aic': -472.450068510614, 'bic': np.float64(-473.04505687100556)}, 4780: {'params': mu          0.935231
omega       0.000650
alpha[1]    0.000000
alpha[2]    0.000000
alpha[3]    0.000000
beta[1]     0.784685
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.000000
beta[5]     0.000000
beta[6]     0.000000
Name: params, dtype: float64, 'loglikelihood': 8.77972563630773, 'aic': 4.440548727384542, 'bic': np.float64(3.845560366992988)}, 4800: {'params': mu          4.189830e-01
omega       6.883311e-10
alpha[1]    2.782649e-12
alpha[2]    6.617722e-12
alpha[3]    1.607542e-11
beta[1]     6.482331e-01
beta[2]     1.562416e-05
beta[3]     1.024579e-07
beta[4]     8.986045e-08
beta[5]     8.977447e-08
beta[6]     8.978506e-08
Name: params, dtype: float64, 'loglikelihood': 7.592201406031634, 'aic': 6.815597187936731, 'bic': np.float64(6.220608827545178)}, 4820: {'params': mu          0.300000
omega       0.000000
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 4840: {'params': mu          2.404616e-01
omega       2.982026e-10
alpha[1]    1.274079e-10
alpha[2]    2.131962e-07
alpha[3]    1.590967e-10
beta[1]     4.612432e-01
beta[2]     4.923251e-01
beta[3]     2.454174e-09
beta[4]     7.961105e-07
beta[5]     1.011303e-07
beta[6]     1.590811e-08
Name: params, dtype: float64, 'loglikelihood': 11.138623000706806, 'aic': -0.2772460014136122, 'bic': np.float64(-0.872234361805166)}, 4860: {'params': mu          0.257058
omega       0.001224
alpha[1]    0.003360
alpha[2]    0.003332
alpha[3]    0.003332
beta[1]     0.081662
beta[2]     0.081663
beta[3]     0.081663
beta[4]     0.081663
beta[5]     0.081663
beta[6]     0.081663
Name: params, dtype: float64, 'loglikelihood': 11.1090187067828, 'aic': -0.21803741356560025, 'bic': np.float64(-0.813025773957154)}, 4880: {'params': mu          0.243072
omega       0.001221
alpha[1]    0.003324
alpha[2]    0.003324
alpha[3]    0.003324
beta[1]     0.081484
beta[2]     0.081486
beta[3]     0.081485
beta[4]     0.081484
beta[5]     0.081482
beta[6]     0.081480
Name: params, dtype: float64, 'loglikelihood': 11.109664777622726, 'aic': -0.2193295552454515, 'bic': np.float64(-0.8143179156370053)}, 4900: {'params': mu          0.100000
omega       0.000000
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 4920: {'params': mu          0.100000
omega       0.000000
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 4940: {'params': mu          0.100000
omega       0.000000
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 4960: {'params': mu          0.100000
omega       0.000000
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}}}
Predicciones Volatilidad_14: {14: {0: array([2.16361556e-05, 2.15422566e-05, 2.15984010e-05, 2.16621630e-05,
       2.16548929e-05, 2.16368275e-05, 2.16246841e-05, 2.16236223e-05,
       2.16301629e-05, 2.16327346e-05, 2.16303581e-05, 2.16283769e-05,
       2.16276808e-05, 2.16279087e-05, 2.16282506e-05, 2.16280940e-05,
       2.16277164e-05, 2.16275000e-05, 2.16274259e-05, 2.16274028e-05,
       2.16273605e-05, 2.16272873e-05, 2.16272210e-05, 2.16271799e-05,
       2.16271532e-05, 2.16271304e-05, 2.16271079e-05, 2.16270870e-05]), 20: array([4.40444681e-05, 4.40754812e-05, 4.40899333e-05, 4.40880528e-05,
       4.40707445e-05, 4.40614703e-05, 4.40579179e-05, 4.40589159e-05,
       4.40575236e-05, 4.40548637e-05, 4.40521430e-05, 4.40506013e-05,
       4.40496906e-05, 4.40490015e-05, 4.40481814e-05, 4.40474104e-05,
       4.40467941e-05, 4.40463499e-05, 4.40459966e-05, 4.40456902e-05,
       4.40454161e-05, 4.40451871e-05, 4.40450029e-05, 4.40448543e-05,
       4.40447303e-05, 4.40446254e-05, 4.40445371e-05, 4.40444643e-05]), 40: array([1.22266124e-05, 1.21556863e-05, 1.21780489e-05, 1.07428211e-05,
       1.06830336e-05, 1.05925013e-05, 1.04888000e-05, 1.03849754e-05,
       1.02765971e-05, 1.01605114e-05, 1.01091143e-05, 1.00620013e-05,
       1.00211318e-05, 9.98840655e-06, 9.96050143e-06, 9.93789755e-06,
       9.92118188e-06, 9.90728636e-06, 9.89598706e-06, 9.88692212e-06,
       9.87955353e-06, 9.87364833e-06, 9.86893930e-06, 9.86512286e-06,
       9.86204810e-06, 9.85957413e-06, 9.85757945e-06, 9.85597546e-06]), 60: array([1.06944202e-05, 1.06474876e-05, 1.05800463e-05, 9.89179442e-06,
       9.87020830e-06, 9.82347187e-06, 9.74732055e-06, 9.69033395e-06,
       9.63048465e-06, 9.57014075e-06, 9.54224605e-06, 9.51597541e-06,
       9.49296664e-06, 9.47510399e-06, 9.45986636e-06, 9.44759483e-06,
       9.43844275e-06, 9.43080850e-06, 9.42461296e-06, 9.41966315e-06,
       9.41563914e-06, 9.41241648e-06, 9.40984447e-06, 9.40775997e-06,
       9.40608227e-06, 9.40473345e-06, 9.40364623e-06, 9.40277234e-06]), 80: array([8.62801378e-06, 8.08769817e-06, 7.69986348e-06, 7.22272276e-06,
       7.20487767e-06, 7.16975517e-06, 7.10462335e-06, 7.02058060e-06,
       6.95493819e-06, 6.90337074e-06, 6.87398623e-06, 6.84766869e-06,
       6.82441306e-06, 6.80513868e-06, 6.78977674e-06, 6.77765919e-06,
       6.76825668e-06, 6.76051140e-06, 6.75420251e-06, 6.74912819e-06,
       6.74505243e-06, 6.74178562e-06, 6.73916415e-06, 6.73704525e-06,
       6.73533813e-06, 6.73396507e-06, 6.73286031e-06, 6.73197171e-06]), 100: array([1.23806773e-05, 1.30657677e-05, 1.35200340e-05, 1.41172062e-05,
       1.42232673e-05, 1.43369825e-05, 1.44703344e-05, 1.45983589e-05,
       1.46999943e-05, 1.47831929e-05, 1.48373494e-05, 1.48839861e-05,
       1.49236023e-05, 1.49556263e-05, 1.49813747e-05, 1.50019363e-05,
       1.50180957e-05, 1.50312976e-05, 1.50419914e-05, 1.50505811e-05,
       1.50574946e-05, 1.50630470e-05, 1.50675062e-05, 1.50711051e-05,
       1.50740028e-05, 1.50763338e-05, 1.50782099e-05, 1.50797193e-05]), 120: array([6.72451182e-05, 6.52002184e-05, 6.11152490e-05, 5.45018696e-05,
       5.44394056e-05, 5.42298866e-05, 5.37372758e-05, 5.30141097e-05,
       5.23095267e-05, 5.17393517e-05, 5.14639409e-05, 5.12115044e-05,
       5.09869962e-05, 5.07988211e-05, 5.06432628e-05, 5.05215966e-05,
       5.04292750e-05, 5.03526870e-05, 5.02901791e-05, 5.02397429e-05,
       5.01990187e-05, 5.01664488e-05, 5.01403529e-05, 5.01192121e-05,
       5.01021611e-05, 5.00884284e-05, 5.00773640e-05, 5.00684614e-05]), 140: array([7.11270066e-07, 7.16274409e-07, 7.15487136e-07, 7.10295388e-07,
       7.12507838e-07, 7.14758978e-07, 7.16537957e-07, 7.17164573e-07,
       7.17282464e-07, 7.17497339e-07, 7.18328761e-07, 7.19002048e-07,
       7.19495733e-07, 7.19842538e-07, 7.20155550e-07, 7.20489800e-07,
       7.20837246e-07, 7.21129038e-07, 7.21376887e-07, 7.21596176e-07,
       7.21800375e-07, 7.21991767e-07, 7.22166543e-07, 7.22321314e-07,
       7.22460162e-07, 7.22586300e-07, 7.22701563e-07, 7.22806467e-07]), 160: array([1.01540355e-06, 1.05306407e-06, 1.11359051e-06, 1.18792625e-06,
       1.20605575e-06, 1.22419387e-06, 1.24109032e-06, 1.25591893e-06,
       1.26938588e-06, 1.28018845e-06, 1.28740810e-06, 1.29357500e-06,
       1.29865666e-06, 1.30276620e-06, 1.30613243e-06, 1.30880692e-06,
       1.31091453e-06, 1.31263307e-06, 1.31401935e-06, 1.31513498e-06,
       1.31603479e-06, 1.31675668e-06, 1.31733666e-06, 1.31780455e-06,
       1.31818110e-06, 1.31848415e-06, 1.31872811e-06, 1.31892435e-06]), 180: array([3.55531703e-06, 3.57990257e-06, 3.60776584e-06, 3.53318563e-06,
       3.54344040e-06, 3.55443638e-06, 3.56643955e-06, 3.56782949e-06,
       3.56652238e-06, 3.56181967e-06, 3.56509718e-06, 3.56757860e-06,
       3.56909348e-06, 3.56942293e-06, 3.56962059e-06, 3.56998370e-06,
       3.57092553e-06, 3.57160079e-06, 3.57206995e-06, 3.57241920e-06,
       3.57276874e-06, 3.57313468e-06, 3.57350059e-06, 3.57380032e-06,
       3.57405671e-06, 3.57428826e-06, 3.57450583e-06, 3.57470794e-06]), 200: array([4.29984227e-06, 4.30920089e-06, 4.31208021e-06, 4.31375305e-06,
       4.31125400e-06, 4.31355993e-06, 4.31539743e-06, 4.31667325e-06,
       4.31730156e-06, 4.31774044e-06, 4.31807389e-06, 4.31863552e-06,
       4.31905447e-06, 4.31935751e-06, 4.31958100e-06, 4.31977031e-06,
       4.31993846e-06, 4.32009267e-06, 4.32021338e-06, 4.32030950e-06,
       4.32038849e-06, 4.32045542e-06, 4.32051217e-06, 4.32055970e-06,
       4.32059841e-06, 4.32063033e-06, 4.32065693e-06, 4.32067918e-06]), 220: array([9.43095785e-06, 9.94224167e-06, 1.04757911e-05, 1.10968840e-05,
       1.12569878e-05, 1.14075578e-05, 1.15434487e-05, 1.16788441e-05,
       1.17937979e-05, 1.18854474e-05, 1.19476755e-05, 1.20001319e-05,
       1.20435161e-05, 1.20790574e-05, 1.21078268e-05, 1.21307079e-05,
       1.21487837e-05, 1.21634875e-05, 1.21753660e-05, 1.21849357e-05,
       1.21926397e-05, 1.21988239e-05, 1.22037935e-05, 1.22078012e-05,
       1.22110276e-05, 1.22136243e-05, 1.22157141e-05, 1.22173953e-05]), 240: array([3.51257507e-06, 3.68852785e-06, 3.75804927e-06, 3.84294343e-06,
       3.89371717e-06, 3.93861566e-06, 3.97817976e-06, 4.01047575e-06,
       4.03435705e-06, 4.05455519e-06, 4.07022747e-06, 4.08303643e-06,
       4.09350276e-06, 4.10186542e-06, 4.10854410e-06, 4.11395396e-06,
       4.11828731e-06, 4.12178509e-06, 4.12460526e-06, 4.12687047e-06,
       4.12869293e-06, 4.13016090e-06, 4.13134162e-06, 4.13229241e-06,
       4.13305774e-06, 4.13367349e-06, 4.13416910e-06, 4.13456802e-06]), 260: array([1.86643289e-05, 1.89722195e-05, 1.92531709e-05, 1.97220173e-05,
       1.99066789e-05, 2.00776430e-05, 2.02281281e-05, 2.03400588e-05,
       2.04373428e-05, 2.05205314e-05, 2.05799508e-05, 2.06296072e-05,
       2.06700230e-05, 2.07020839e-05, 2.07283274e-05, 2.07494579e-05,
       2.07661999e-05, 2.07797868e-05, 2.07907264e-05, 2.07995128e-05,
       2.08066051e-05, 2.08123069e-05, 2.08168881e-05, 2.08205808e-05,
       2.08235523e-05, 2.08259432e-05, 2.08278684e-05, 2.08294174e-05]), 280: array([2.01083666e-06, 2.02135052e-06, 2.03168501e-06, 2.01187296e-06,
       2.01758701e-06, 2.02346185e-06, 2.02909818e-06, 2.03125567e-06,
       2.03244032e-06, 2.03255711e-06, 2.03494732e-06, 2.03695606e-06,
       2.03852295e-06, 2.03962668e-06, 2.04060494e-06, 2.04155604e-06,
       2.04260103e-06, 2.04349112e-06, 2.04425227e-06, 2.04492013e-06,
       2.04553661e-06, 2.04611057e-06, 2.04664053e-06, 2.04711081e-06,
       2.04753232e-06, 2.04791427e-06, 2.04826284e-06, 2.04858019e-06]), 300: array([3.24306907e-06, 3.32217409e-06, 3.48202531e-06, 3.68080764e-06,
       3.72071972e-06, 3.76211587e-06, 3.80258407e-06, 3.83867825e-06,
       3.87236736e-06, 3.89923457e-06, 3.91659928e-06, 3.93158800e-06,
       3.94400965e-06, 3.95406593e-06, 3.96233310e-06, 3.96888106e-06,
       3.97402148e-06, 3.97822296e-06, 3.98161403e-06, 3.98434311e-06,
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       0.00010923, 0.00010923, 0.00010923]), 4580: array([8.09497972e-05, 8.07593335e-05, 8.05526773e-05, 8.03902488e-05,
       8.02305616e-05, 8.01061775e-05, 8.00190447e-05, 7.99417968e-05,
       7.98740696e-05, 7.98178769e-05, 7.97704633e-05, 7.97323179e-05,
       7.97013139e-05, 7.96749777e-05, 7.96528694e-05, 7.96345402e-05,
       7.96193453e-05, 7.96068187e-05, 7.95964162e-05, 7.95877226e-05,
       7.95804914e-05, 7.95744928e-05, 7.95695160e-05, 7.95653859e-05,
       7.95619520e-05, 7.95590956e-05, 7.95567230e-05, 7.95547531e-05]), 4600: array([4.57384681e-05, 2.89007456e-05, 1.83282747e-05, 1.16897795e-05,
       7.52144266e-06, 4.90412791e-06, 3.26070588e-06, 2.22879485e-06,
       1.58085393e-06, 1.17400932e-06, 9.18550029e-07, 7.58146151e-07,
       6.57427938e-07, 5.94186583e-07, 5.54477092e-07, 5.29543350e-07,
       5.13887357e-07, 5.04056898e-07, 4.97884315e-07, 4.94008527e-07,
       4.91574904e-07, 4.90046823e-07, 4.89087335e-07, 4.88484869e-07,
       4.88106578e-07, 4.87869048e-07, 4.87719902e-07, 4.87626252e-07]), 4620: array([9.53628465e-07, 9.88221938e-07, 1.03127656e-06, 1.08031060e-06,
       1.08425398e-06, 1.08884300e-06, 1.09424758e-06, 1.10220767e-06,
       1.10910387e-06, 1.11434596e-06, 1.11738761e-06, 1.12005629e-06,
       1.12234712e-06, 1.12428551e-06, 1.12584926e-06, 1.12707272e-06,
       1.12802410e-06, 1.12880517e-06, 1.12943967e-06, 1.12995209e-06,
       1.13036396e-06, 1.13069361e-06, 1.13095825e-06, 1.13117204e-06,
       1.13134425e-06, 1.13148286e-06, 1.13159437e-06, 1.13168404e-06]), 4640: array([3.67950590e-05, 3.70629949e-05, 3.73416997e-05, 3.68918074e-05,
       3.70159138e-05, 3.71269157e-05, 3.72220430e-05, 3.72580145e-05,
       3.72747482e-05, 3.72697732e-05, 3.73007998e-05, 3.73242084e-05,
       3.73404857e-05, 3.73503943e-05, 3.73581041e-05, 3.73650245e-05,
       3.73728853e-05, 3.73788473e-05, 3.73833786e-05, 3.73869428e-05,
       3.73899745e-05, 3.73926143e-05, 3.73948983e-05, 3.73967226e-05,
       3.73982049e-05, 3.73994344e-05, 3.74004696e-05, 3.74013392e-05]), 4660: array([0.00013979, 0.00014001, 0.0001395 , 0.00013932, 0.00013935,
       0.0001394 , 0.0001394 , 0.00013937, 0.00013931, 0.0001393 ,
       0.0001393 , 0.00013929, 0.00013928, 0.00013927, 0.00013927,
       0.00013926, 0.00013926, 0.00013926, 0.00013925, 0.00013925,
       0.00013925, 0.00013925, 0.00013925, 0.00013925, 0.00013924,
       0.00013924, 0.00013924, 0.00013924]), 4680: array([0.00091435, 0.00095111, 0.00098787, 0.00102462, 0.00106138,
       0.00109813, 0.00113489, 0.00117165, 0.0012084 , 0.00124516,
       0.00128192, 0.00131867, 0.00135543, 0.00139218, 0.00142894,
       0.0014657 , 0.00150245, 0.00153921, 0.00157597, 0.00161272,
       0.00164948, 0.00168623, 0.00172299, 0.00175975, 0.0017965 ,
       0.00183326, 0.00187002, 0.00190677]), 4700: array([0.00018593, 0.00018548, 0.00018542, 0.00018569, 0.0001855 ,
       0.00018535, 0.00018524, 0.00018518, 0.00018516, 0.00018513,
       0.00018509, 0.00018505, 0.00018503, 0.00018501, 0.000185  ,
       0.00018498, 0.00018497, 0.00018496, 0.00018495, 0.00018495,
       0.00018494, 0.00018494, 0.00018493, 0.00018493, 0.00018493,
       0.00018493, 0.00018493, 0.00018492]), 4720: array([2.03816584e-05, 2.03624129e-05, 2.03329599e-05, 2.03841288e-05,
       2.04101605e-05, 2.04255750e-05, 2.04266584e-05, 2.04304752e-05,
       2.04361013e-05, 2.04445596e-05, 2.04495545e-05, 2.04528353e-05,
       2.04551173e-05, 2.04574767e-05, 2.04597082e-05, 2.04616590e-05,
       2.04630773e-05, 2.04642003e-05, 2.04651434e-05, 2.04659738e-05,
       2.04666774e-05, 2.04672548e-05, 2.04677189e-05, 2.04681037e-05,
       2.04684273e-05, 2.04686994e-05, 2.04689252e-05, 2.04691115e-05]), 4740: array([1.23778265e-05, 1.25150163e-05, 1.26543658e-05, 1.27954346e-05,
       1.27886437e-05, 1.27980905e-05, 1.28268343e-05, 1.28513780e-05,
       1.28723783e-05, 1.28882314e-05, 1.28969644e-05, 1.29054195e-05,
       1.29129886e-05, 1.29189468e-05, 1.29237908e-05, 1.29275861e-05,
       1.29305270e-05, 1.29329772e-05, 1.29349675e-05, 1.29365585e-05,
       1.29378412e-05, 1.29388680e-05, 1.29396921e-05, 1.29403593e-05,
       1.29408962e-05, 1.29413279e-05, 1.29416754e-05, 1.29419549e-05]), 4760: array([1.21410201e-04, 1.02066746e-04, 8.63245728e-05, 7.35119510e-05,
       6.30842578e-05, 5.45975652e-05, 4.76905776e-05, 4.20692504e-05,
       3.74942720e-05, 3.37708757e-05, 3.07405489e-05, 2.82742843e-05,
       2.62670879e-05, 2.46335091e-05, 2.33040032e-05, 2.22219702e-05,
       2.13413459e-05, 2.06246401e-05, 2.00413413e-05, 1.95666171e-05,
       1.91802577e-05, 1.88658149e-05, 1.86099021e-05, 1.84016247e-05,
       1.82321159e-05, 1.80941593e-05, 1.79818818e-05, 1.78905035e-05]), 4780: array([4.38297193e-06, 4.57776696e-06, 4.77632936e-06, 4.97815351e-06,
       4.96321957e-06, 4.96811734e-06, 4.99663743e-06, 5.02855296e-06,
       5.05544781e-06, 5.07522576e-06, 5.08531860e-06, 5.09520793e-06,
       5.10421313e-06, 5.11152440e-06, 5.11742003e-06, 5.12199945e-06,
       5.12552389e-06, 5.12846745e-06, 5.13086692e-06, 5.13279077e-06,
       5.13433855e-06, 5.13557588e-06, 5.13656864e-06, 5.13737273e-06,
       5.13802027e-06, 5.13854090e-06, 5.13895989e-06, 5.13929677e-06]), 4800: array([0.00029308, 0.00029377, 0.00029328, 0.00029284, 0.00029248,
       0.00029246, 0.00029245, 0.0002924 , 0.00029229, 0.0002922 ,
       0.00029215, 0.00029212, 0.0002921 , 0.00029207, 0.00029204,
       0.00029202, 0.000292  , 0.00029199, 0.00029198, 0.00029197,
       0.00029196, 0.00029196, 0.00029195, 0.00029195, 0.00029194,
       0.00029194, 0.00029194, 0.00029194]), 4820: array([0.0050434 , 0.0050434 , 0.0050434 , 0.0050434 , 0.0050434 ,
       0.00581224, 0.00581224, 0.00581224, 0.00581224, 0.00581224,
       0.00581224, 0.00658107, 0.00658107, 0.00658107, 0.00658107,
       0.00658107, 0.00658107, 0.00734991, 0.00734991, 0.00734991,
       0.00734991, 0.00734991, 0.00734991, 0.00811874, 0.00811874,
       0.00811874, 0.00811874, 0.00811874]), 4840: array([0.00122794, 0.00122463, 0.00122099, 0.00122386, 0.0012234 ,
       0.00122305, 0.00122249, 0.00122204, 0.00122183, 0.00122189,
       0.00122173, 0.00122159, 0.00122147, 0.00122139, 0.00122133,
       0.00122129, 0.00122124, 0.0012212 , 0.00122117, 0.00122114,
       0.00122112, 0.00122111, 0.00122109, 0.00122108, 0.00122107,
       0.00122106, 0.00122105, 0.00122105]), 4860: array([0.00032052, 0.00036434, 0.00036434, 0.00036434, 0.00036434,
       0.00040817, 0.00040817, 0.00040817, 0.00040817, 0.000452  ,
       0.000452  , 0.000452  , 0.000452  , 0.00049582, 0.00049582,
       0.00049582, 0.00049582, 0.00053965, 0.00053965, 0.00053965,
       0.00053965, 0.00058347, 0.00058347, 0.00058347, 0.00058347,
       0.0006273 , 0.0006273 , 0.0006273 ]), 4880: array([0.00035377, 0.00035377, 0.00035377, 0.0004056 , 0.0004056 ,
       0.0004056 , 0.0004056 , 0.0004056 , 0.00045743, 0.00045743,
       0.00045743, 0.00045743, 0.00045743, 0.00050926, 0.00050926,
       0.00050926, 0.00050926, 0.00050926, 0.00056109, 0.00056109,
       0.00056109, 0.00056109, 0.00056109, 0.00061292, 0.00061292,
       0.00061292, 0.00061292, 0.00061292]), 4900: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]), 4920: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]), 4940: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])}}
Resultados Modelo Volatilidad_14: {14: {0: {'params': mu          0.040216
omega       0.000011
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 55.34037494221111, 'aic': -88.68074988442223, 'bic': np.float64(-81.65111925865438)}, 20: {'params': mu          0.022789
omega       0.000022
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 50.36735059330688, 'aic': -78.73470118661376, 'bic': np.float64(-71.70507056084591)}, 40: {'params': mu          0.017452
omega       0.000005
alpha[1]    0.072342
alpha[2]    0.066262
alpha[3]    0.066261
beta[1]     0.049696
beta[2]     0.049696
beta[3]     0.049696
beta[4]     0.049696
beta[5]     0.049696
beta[6]     0.049696
Name: params, dtype: float64, 'loglikelihood': 62.004697409958425, 'aic': -102.00939481991685, 'bic': np.float64(-94.979764194149)}, 60: {'params': mu          0.032307
omega       0.000005
alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 61.36351539787141, 'aic': -100.72703079574282, 'bic': np.float64(-93.69740016997497)}, 80: {'params': mu          0.021169
omega       0.000003
alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 63.569674892842215, 'aic': -105.13934978568443, 'bic': np.float64(-98.10971915991658)}, 100: {'params': mu          0.022505
omega       0.000008
alpha[1]    0.066667
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 58.11884474553111, 'aic': -94.23768949106223, 'bic': np.float64(-87.20805886529439)}, 120: {'params': mu          0.025055
omega       0.000025
alpha[1]    0.079440
alpha[2]    0.065754
alpha[3]    0.065754
beta[1]     0.049316
beta[2]     0.049316
beta[3]     0.049316
beta[4]     0.049316
beta[5]     0.049316
beta[6]     0.049316
Name: params, dtype: float64, 'loglikelihood': 51.62223940847806, 'aic': -81.24447881695612, 'bic': np.float64(-74.21484819118828)}, 140: {'params': mu          2.667154e-02
omega       2.171445e-07
alpha[1]    3.333381e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     1.150000e-01
beta[2]     1.150000e-01
beta[3]     1.150000e-01
beta[4]     1.150000e-01
beta[5]     1.150000e-01
beta[6]     1.150000e-01
Name: params, dtype: float64, 'loglikelihood': 79.17174414151769, 'aic': -136.34348828303538, 'bic': np.float64(-129.31385765726753)}, 160: {'params': mu          1.491676e-02
omega       6.598668e-07
alpha[1]    6.666676e-02
alpha[2]    6.666666e-02
alpha[3]    6.666666e-02
beta[1]     5.000000e-02
beta[2]     5.000000e-02
beta[3]     5.000000e-02
beta[4]     5.000000e-02
beta[5]     5.000000e-02
beta[6]     5.000000e-02
Name: params, dtype: float64, 'loglikelihood': 75.399176800746, 'aic': -128.798353601492, 'bic': np.float64(-121.76872297572416)}, 180: {'params': mu          0.013666
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 67.9088675087767, 'aic': -113.81773501755339, 'bic': np.float64(-106.78810439178554)}, 200: {'params': mu          0.023343
omega       0.000002
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 66.63566451877337, 'aic': -111.27132903754674, 'bic': np.float64(-104.24169841177888)}, 220: {'params': mu          0.010124
omega       0.000006
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 59.89065344432055, 'aic': -97.7813068886411, 'bic': np.float64(-90.75167626287325)}, 240: {'params': mu          0.015690
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 67.47408462722902, 'aic': -112.94816925445804, 'bic': np.float64(-105.91853862869019)}, 260: {'params': mu          0.020194
omega       0.000010
alpha[1]    0.066671
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 56.01721352983877, 'aic': -90.03442705967754, 'bic': np.float64(-83.00479643390969)}, 280: {'params': mu          2.648345e-02
omega       6.154904e-07
alpha[1]    3.333341e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     1.150000e-01
beta[2]     1.150000e-01
beta[3]     1.150000e-01
beta[4]     1.150000e-01
beta[5]     1.150000e-01
beta[6]     1.150000e-01
Name: params, dtype: float64, 'loglikelihood': 71.90490908223751, 'aic': -121.80981816447502, 'bic': np.float64(-114.78018753870717)}, 300: {'params': mu          0.014054
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 67.35743477568053, 'aic': -112.71486955136106, 'bic': np.float64(-105.68523892559321)}, 320: {'params': mu          0.023746
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 63.256830713493436, 'aic': -104.51366142698687, 'bic': np.float64(-97.48403080121903)}, 340: {'params': mu          0.017212
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 65.86975416130633, 'aic': -109.73950832261266, 'bic': np.float64(-102.70987769684481)}, 360: {'params': mu          0.040284
omega       0.000010
alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 56.13833483675054, 'aic': -90.27666967350108, 'bic': np.float64(-83.24703904773324)}, 380: {'params': mu          0.021753
omega       0.000017
alpha[1]    0.457468
alpha[2]    0.000000
alpha[3]    0.000000
beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.000000
beta[5]     0.000000
beta[6]     0.000000
Name: params, dtype: float64, 'loglikelihood': 54.14086867827095, 'aic': -86.2817373565419, 'bic': np.float64(-79.25210673077405)}, 400: {'params': mu          0.023295
omega       0.000016
alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 52.869197665605995, 'aic': -83.73839533121199, 'bic': np.float64(-76.70876470544414)}, 420: {'params': mu          0.024479
omega       0.000002
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 62.780701639699544, 'aic': -103.56140327939909, 'bic': np.float64(-96.53177265363124)}, 440: {'params': mu          0.009008
omega       0.000010
alpha[1]    0.081911
alpha[2]    0.065744
alpha[3]    0.065744
beta[1]     0.049308
beta[2]     0.049308
beta[3]     0.049308
beta[4]     0.049308
beta[5]     0.049308
beta[6]     0.049308
Name: params, dtype: float64, 'loglikelihood': 57.915416784819165, 'aic': -93.83083356963833, 'bic': np.float64(-86.80120294387049)}, 460: {'params': mu          0.016861
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 67.85809911015056, 'aic': -113.71619822030112, 'bic': np.float64(-106.68656759453327)}, 480: {'params': mu          1.891169e-02
omega       4.494330e-05
alpha[1]    9.999941e-01
alpha[2]    4.291856e-07
alpha[3]    4.343904e-07
beta[1]     3.276357e-07
beta[2]     3.327900e-07
beta[3]     3.381381e-07
beta[4]     3.441545e-07
beta[5]     3.506618e-07
beta[6]     3.567028e-07
Name: params, dtype: float64, 'loglikelihood': 38.35556510117505, 'aic': -54.711130202350105, 'bic': np.float64(-47.68149957658226)}, 500: {'params': mu          0.020919
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alpha[1]    0.532384
alpha[2]    0.033346
alpha[3]    0.033346
beta[1]     0.025010
beta[2]     0.025010
beta[3]     0.025010
beta[4]     0.025010
beta[5]     0.025010
beta[6]     0.025010
Name: params, dtype: float64, 'loglikelihood': 42.59850218333154, 'aic': -63.19700436666308, 'bic': np.float64(-56.167373740895236)}, 520: {'params': mu          0.015224
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alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 62.87598293661769, 'aic': -103.75196587323538, 'bic': np.float64(-96.72233524746753)}, 540: {'params': mu          3.971006e-02
omega       1.953060e-05
alpha[1]    8.025387e-01
alpha[2]    4.561932e-07
alpha[3]    4.577841e-07
beta[1]     3.430779e-07
beta[2]     3.432382e-07
beta[3]     3.432804e-07
beta[4]     3.431658e-07
beta[5]     3.430277e-07
beta[6]     3.428613e-07
Name: params, dtype: float64, 'loglikelihood': 46.90263989449062, 'aic': -71.80527978898124, 'bic': np.float64(-64.77564916321339)}, 560: {'params': mu          0.030813
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 52.31774987384968, 'aic': -82.63549974769936, 'bic': np.float64(-75.6058691219315)}, 580: {'params': mu          0.023633
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alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 49.60572848383033, 'aic': -77.21145696766067, 'bic': np.float64(-70.18182634189282)}, 600: {'params': mu          0.034662
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 65.54561276319149, 'aic': -109.09122552638297, 'bic': np.float64(-102.06159490061512)}, 620: {'params': mu          0.026923
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alpha[1]    0.180756
alpha[2]    0.058517
alpha[3]    0.058517
beta[1]     0.043888
beta[2]     0.043888
beta[3]     0.043888
beta[4]     0.043888
beta[5]     0.043888
beta[6]     0.043888
Name: params, dtype: float64, 'loglikelihood': 56.410379861248536, 'aic': -90.82075972249707, 'bic': np.float64(-83.79112909672924)}, 640: {'params': mu          6.239820e-02
omega       1.932835e-05
alpha[1]    9.999992e-01
alpha[2]    5.635472e-07
alpha[3]    5.635507e-07
beta[1]     4.226459e-07
beta[2]     4.226645e-07
beta[3]     4.227161e-07
beta[4]     4.227338e-07
beta[5]     4.227583e-07
beta[6]     4.227413e-07
Name: params, dtype: float64, 'loglikelihood': 47.37978271796908, 'aic': -72.75956543593816, 'bic': np.float64(-65.7299348101703)}, 660: {'params': mu          0.036294
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alpha[1]    0.405264
alpha[2]    0.042481
alpha[3]    0.042481
beta[1]     0.031861
beta[2]     0.031861
beta[3]     0.031861
beta[4]     0.031861
beta[5]     0.031861
beta[6]     0.031861
Name: params, dtype: float64, 'loglikelihood': 53.67597983268456, 'aic': -85.35195966536912, 'bic': np.float64(-78.32232903960127)}, 680: {'params': mu          4.499426e-02
omega       1.377578e-05
alpha[1]    9.999974e-01
alpha[2]    2.829921e-07
alpha[3]    2.829926e-07
beta[1]     2.122510e-07
beta[2]     2.122616e-07
beta[3]     2.122757e-07
beta[4]     2.122900e-07
beta[5]     2.122905e-07
beta[6]     2.122521e-07
Name: params, dtype: float64, 'loglikelihood': 47.33101185102366, 'aic': -72.66202370204732, 'bic': np.float64(-65.63239307627947)}, 700: {'params': mu          2.705622e-02
omega       8.083256e-07
alpha[1]    3.333351e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 73.49289896664362, 'aic': -124.98579793328724, 'bic': np.float64(-117.9561673075194)}, 720: {'params': mu          0.022833
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alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
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beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 55.96179598627159, 'aic': -89.92359197254318, 'bic': np.float64(-82.89396134677534)}, 740: {'params': mu          0.049468
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alpha[1]    0.066668
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 57.389337618224424, 'aic': -92.77867523644885, 'bic': np.float64(-85.74904461068101)}, 760: {'params': mu          0.033478
omega       0.000004
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 62.129965259133215, 'aic': -102.25993051826643, 'bic': np.float64(-95.23029989249858)}, 780: {'params': mu          3.641004e-02
omega       5.395733e-07
alpha[1]    6.666676e-02
alpha[2]    6.666666e-02
alpha[3]    6.666666e-02
beta[1]     5.000000e-02
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beta[3]     5.000000e-02
beta[4]     5.000000e-02
beta[5]     5.000000e-02
beta[6]     5.000000e-02
Name: params, dtype: float64, 'loglikelihood': 76.33348394814224, 'aic': -130.6669678962845, 'bic': np.float64(-123.63733727051664)}, 800: {'params': mu          0.026161
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 69.24696558393089, 'aic': -116.49393116786177, 'bic': np.float64(-109.46430054209392)}, 820: {'params': mu          0.036018
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 58.962135993134986, 'aic': -95.92427198626997, 'bic': np.float64(-88.89464136050213)}, 840: {'params': mu          3.844122e-02
omega       5.804678e-06
alpha[1]    5.506237e-01
alpha[2]    0.000000e+00
alpha[3]    4.493767e-01
beta[1]     0.000000e+00
beta[2]     8.996207e-09
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 55.71902542004055, 'aic': -89.4380508400811, 'bic': np.float64(-82.40842021431325)}, 860: {'params': mu          0.026888
omega       0.000001
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 66.5459895094089, 'aic': -111.0919790188178, 'bic': np.float64(-104.06234839304994)}, 880: {'params': mu          0.032496
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alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 68.89177348670748, 'aic': -115.78354697341496, 'bic': np.float64(-108.7539163476471)}, 900: {'params': mu          0.044177
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 57.62573267038388, 'aic': -93.25146534076777, 'bic': np.float64(-86.22183471499991)}, 920: {'params': mu          0.039401
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alpha[1]    0.168436
alpha[2]    0.059397
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beta[1]     0.044548
beta[2]     0.044548
beta[3]     0.044548
beta[4]     0.044548
beta[5]     0.044548
beta[6]     0.044548
Name: params, dtype: float64, 'loglikelihood': 52.260035777997246, 'aic': -82.52007155599449, 'bic': np.float64(-75.49044093022664)}, 940: {'params': mu          0.033545
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 71.09868034280154, 'aic': -120.19736068560309, 'bic': np.float64(-113.16773005983524)}, 960: {'params': mu          0.033846
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 70.53612934719052, 'aic': -119.07225869438105, 'bic': np.float64(-112.0426280686132)}, 980: {'params': mu          0.029079
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alpha[1]    0.279263
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alpha[3]    0.049813
beta[1]     0.037360
beta[2]     0.037360
beta[3]     0.037360
beta[4]     0.037360
beta[5]     0.037360
beta[6]     0.037360
Name: params, dtype: float64, 'loglikelihood': 49.14246985093464, 'aic': -76.28493970186928, 'bic': np.float64(-69.25530907610144)}, 1000: {'params': mu          0.054685
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 63.230215369149235, 'aic': -104.46043073829847, 'bic': np.float64(-97.43080011253062)}, 1020: {'params': mu          7.286461e-02
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alpha[1]    7.979997e-01
alpha[2]    2.400461e-04
alpha[3]    2.400488e-04
beta[1]     1.800347e-04
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beta[3]     1.800405e-04
beta[4]     1.800461e-04
beta[5]     1.800509e-04
beta[6]     1.800580e-04
Name: params, dtype: float64, 'loglikelihood': 51.2505426791876, 'aic': -80.5010853583752, 'bic': np.float64(-73.47145473260736)}, 1040: {'params': mu          0.048081
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alpha[1]    0.003336
alpha[2]    0.003333
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beta[1]     0.081666
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beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 50.19047308229301, 'aic': -78.38094616458602, 'bic': np.float64(-71.35131553881817)}, 1060: {'params': mu          0.032822
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 56.52147584127451, 'aic': -91.04295168254902, 'bic': np.float64(-84.01332105678117)}, 1080: {'params': mu          0.030294
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 59.35040028848248, 'aic': -96.70080057696497, 'bic': np.float64(-89.67116995119713)}, 1100: {'params': mu          0.037316
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alpha[1]    0.066713
alpha[2]    0.066663
alpha[3]    0.066663
beta[1]     0.049997
beta[2]     0.049997
beta[3]     0.049997
beta[4]     0.049997
beta[5]     0.049997
beta[6]     0.049997
Name: params, dtype: float64, 'loglikelihood': 55.74427598455839, 'aic': -89.48855196911678, 'bic': np.float64(-82.45892134334895)}, 1120: {'params': mu          0.049135
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 60.90085650081433, 'aic': -99.80171300162866, 'bic': np.float64(-92.7720823758608)}, 1140: {'params': mu          0.053482
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alpha[1]    0.066670
alpha[2]    0.066666
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 49.17096663134124, 'aic': -76.34193326268247, 'bic': np.float64(-69.31230263691464)}, 1160: {'params': mu          0.054889
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alpha[1]    0.999992
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beta[1]     0.000004
beta[2]     0.000004
beta[3]     0.000004
beta[4]     0.000004
beta[5]     0.000004
beta[6]     0.000004
Name: params, dtype: float64, 'loglikelihood': 51.14114525675333, 'aic': -80.28229051350667, 'bic': np.float64(-73.25265988773882)}, 1180: {'params': mu          3.517568e-02
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alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 72.0704235308125, 'aic': -122.14084706162501, 'bic': np.float64(-115.11121643585716)}, 1200: {'params': mu          0.040786
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 63.45979244762785, 'aic': -104.9195848952557, 'bic': np.float64(-97.88995426948784)}, 1220: {'params': mu          0.033645
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 67.94755351432461, 'aic': -113.89510702864922, 'bic': np.float64(-106.86547640288137)}, 1240: {'params': mu          0.019873
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 57.45235686985911, 'aic': -92.90471373971822, 'bic': np.float64(-85.87508311395038)}, 1260: {'params': mu          0.018549
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alpha[1]    0.066670
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 56.748383769047, 'aic': -91.496767538094, 'bic': np.float64(-84.46713691232617)}, 1280: {'params': mu          0.033198
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alpha[1]    0.066680
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beta[3]     0.049999
beta[4]     0.049999
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Name: params, dtype: float64, 'loglikelihood': 43.513050189577, 'aic': -65.026100379154, 'bic': np.float64(-57.99646975338616)}, 1300: {'params': mu          2.020256e-02
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alpha[1]    3.333433e-03
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alpha[3]    3.333333e-03
beta[1]     8.166666e-02
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beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 77.47256722079184, 'aic': -132.9451344415837, 'bic': np.float64(-125.91550381581584)}, 1320: {'params': mu          0.032648
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alpha[1]    0.003335
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beta[1]     0.115000
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beta[3]     0.115000
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beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 56.95609695022865, 'aic': -91.9121939004573, 'bic': np.float64(-84.88256327468946)}, 1340: {'params': mu          0.012158
omega       0.000001
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 71.43402446491237, 'aic': -120.86804892982474, 'bic': np.float64(-113.83841830405689)}, 1360: {'params': mu          0.018684
omega       0.000003
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 63.34135855650591, 'aic': -104.68271711301182, 'bic': np.float64(-97.65308648724397)}, 1380: {'params': mu          0.035350
omega       0.000004
alpha[1]    0.066666
alpha[2]    0.066668
alpha[3]    0.066668
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 63.06900123260375, 'aic': -104.1380024652075, 'bic': np.float64(-97.10837183943966)}, 1400: {'params': mu          0.043684
omega       0.000007
alpha[1]    0.082259
alpha[2]    0.065553
alpha[3]    0.065553
beta[1]     0.049165
beta[2]     0.049165
beta[3]     0.049165
beta[4]     0.049165
beta[5]     0.049165
beta[6]     0.049165
Name: params, dtype: float64, 'loglikelihood': 58.76239247918835, 'aic': -95.5247849583767, 'bic': np.float64(-88.49515433260885)}, 1420: {'params': mu          0.033538
omega       0.000006
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 59.50014522356663, 'aic': -97.00029044713327, 'bic': np.float64(-89.97065982136542)}, 1440: {'params': mu          0.041454
omega       0.000019
alpha[1]    0.320427
alpha[2]    0.048541
alpha[3]    0.048541
beta[1]     0.036406
beta[2]     0.036406
beta[3]     0.036406
beta[4]     0.036406
beta[5]     0.036406
beta[6]     0.036406
Name: params, dtype: float64, 'loglikelihood': 50.927660300673814, 'aic': -79.85532060134763, 'bic': np.float64(-72.82568997557979)}, 1460: {'params': mu          0.184027
omega       0.000012
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 54.710292413360655, 'aic': -87.42058482672131, 'bic': np.float64(-80.39095420095347)}, 1480: {'params': mu          0.029319
omega       0.000001
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 70.37325312894257, 'aic': -118.74650625788513, 'bic': np.float64(-111.71687563211728)}, 1500: {'params': mu          0.022132
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 71.07575252191504, 'aic': -120.15150504383007, 'bic': np.float64(-113.12187441806222)}, 1520: {'params': mu          0.031098
omega       0.000003
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 64.21209904120833, 'aic': -106.42419808241667, 'bic': np.float64(-99.39456745664882)}, 1540: {'params': mu          0.028675
omega       0.000021
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 50.7904616577147, 'aic': -79.5809233154294, 'bic': np.float64(-72.55129268966155)}, 1560: {'params': mu          0.022447
omega       0.000020
alpha[1]    0.182526
alpha[2]    0.056915
alpha[3]    0.056915
beta[1]     0.042686
beta[2]     0.042686
beta[3]     0.042686
beta[4]     0.042686
beta[5]     0.042686
beta[6]     0.042686
Name: params, dtype: float64, 'loglikelihood': 50.95914870058827, 'aic': -79.91829740117655, 'bic': np.float64(-72.8886667754087)}, 1580: {'params': mu          0.022141
omega       0.000003
alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 64.39850429844952, 'aic': -106.79700859689905, 'bic': np.float64(-99.7673779711312)}, 1600: {'params': mu          0.048222
omega       0.000013
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 50.60299249099479, 'aic': -79.20598498198957, 'bic': np.float64(-72.17635435622174)}, 1620: {'params': mu          0.025792
omega       0.000020
alpha[1]    1.000000
alpha[2]    0.000000
alpha[3]    0.000000
beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.000000
beta[5]     0.000000
beta[6]     0.000000
Name: params, dtype: float64, 'loglikelihood': 49.68866740431555, 'aic': -77.3773348086311, 'bic': np.float64(-70.34770418286325)}, 1640: {'params': mu          0.019687
omega       0.000065
alpha[1]    0.066681
alpha[2]    0.066665
alpha[3]    0.066665
beta[1]     0.049999
beta[2]     0.049999
beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 43.339496452923264, 'aic': -64.67899290584653, 'bic': np.float64(-57.649362280078684)}, 1660: {'params': mu          0.030530
omega       0.000006
alpha[1]    0.076908
alpha[2]    0.065936
alpha[3]    0.065936
beta[1]     0.049452
beta[2]     0.049452
beta[3]     0.049452
beta[4]     0.049452
beta[5]     0.049452
beta[6]     0.049452
Name: params, dtype: float64, 'loglikelihood': 59.985163940181145, 'aic': -97.97032788036229, 'bic': np.float64(-90.94069725459445)}, 1680: {'params': mu          3.350282e-02
omega       7.632662e-07
alpha[1]    8.706385e-01
alpha[2]    1.689202e-04
alpha[3]    1.708743e-04
beta[1]     1.689202e-04
beta[2]     1.705357e-04
beta[3]     1.733791e-04
beta[4]     1.690380e-04
beta[5]     1.689203e-04
beta[6]     1.733861e-04
Name: params, dtype: float64, 'loglikelihood': 55.48120303754629, 'aic': -88.96240607509257, 'bic': np.float64(-81.93277544932474)}, 1700: {'params': mu          0.065192
omega       0.000011
alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 55.252696053190654, 'aic': -88.50539210638131, 'bic': np.float64(-81.47576148061347)}, 1720: {'params': mu          0.068882
omega       0.000042
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115009
beta[2]     0.115008
beta[3]     0.115008
beta[4]     0.115006
beta[5]     0.115004
beta[6]     0.114999
Name: params, dtype: float64, 'loglikelihood': 42.39777453075184, 'aic': -62.79554906150368, 'bic': np.float64(-55.765918435735834)}, 1740: {'params': mu          0.034421
omega       0.000008
alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 58.495680970291644, 'aic': -94.99136194058329, 'bic': np.float64(-87.96173131481544)}, 1760: {'params': mu          0.051965
omega       0.000013
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 54.21792567745539, 'aic': -86.43585135491078, 'bic': np.float64(-79.40622072914294)}, 1780: {'params': mu          0.019771
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 69.04552670433421, 'aic': -116.09105340866842, 'bic': np.float64(-109.06142278290056)}, 1800: {'params': mu          0.036499
omega       0.000043
alpha[1]    0.066685
alpha[2]    0.066664
alpha[3]    0.066664
beta[1]     0.049998
beta[2]     0.049998
beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 46.09603567611484, 'aic': -70.19207135222968, 'bic': np.float64(-63.16244072646183)}, 1820: {'params': mu          1.048499e-02
omega       3.654784e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     1.150000e-01
beta[2]     1.150000e-01
beta[3]     1.150000e-01
beta[4]     1.150000e-01
beta[5]     1.150000e-01
beta[6]     1.150000e-01
Name: params, dtype: float64, 'loglikelihood': 75.52819417258178, 'aic': -129.05638834516355, 'bic': np.float64(-122.0267577193957)}, 1840: {'params': mu          0.031075
omega       0.000022
alpha[1]    0.066671
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 51.267750291837565, 'aic': -80.53550058367513, 'bic': np.float64(-73.5058699579073)}, 1860: {'params': mu          0.021320
omega       0.000008
alpha[1]    0.066690
alpha[2]    0.066665
alpha[3]    0.066665
beta[1]     0.049999
beta[2]     0.049999
beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 57.96435553193954, 'aic': -93.92871106387908, 'bic': np.float64(-86.89908043811124)}, 1880: {'params': mu          3.469190e-02
omega       5.216178e-10
alpha[1]    3.642990e-01
alpha[2]    1.192733e-02
alpha[3]    1.192733e-02
beta[1]     8.945496e-03
beta[2]     8.945497e-03
beta[3]     8.945497e-03
beta[4]     8.945498e-03
beta[5]     8.945498e-03
beta[6]     8.945499e-03
Name: params, dtype: float64, 'loglikelihood': 47.67275276317134, 'aic': -73.34550552634268, 'bic': np.float64(-66.31587490057484)}, 1900: {'params': mu          0.043993
omega       0.000018
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 51.65223089623253, 'aic': -81.30446179246506, 'bic': np.float64(-74.27483116669723)}, 1920: {'params': mu          3.965766e-02
omega       3.839429e-06
alpha[1]    6.514927e-01
alpha[2]    1.453504e-13
alpha[3]    2.917135e-13
beta[1]     9.778270e-14
beta[2]     2.155881e-13
beta[3]     1.243140e-13
beta[4]     3.485073e-01
beta[5]     1.518727e-14
beta[6]     2.308878e-15
Name: params, dtype: float64, 'loglikelihood': 54.794527159932365, 'aic': -87.58905431986473, 'bic': np.float64(-80.55942369409689)}, 1940: {'params': mu          5.931768e-02
omega       4.675329e-05
alpha[1]    1.000000e+00
alpha[2]    8.029664e-04
alpha[3]    8.177605e-04
beta[1]     9.345237e-12
beta[2]     1.299154e-11
beta[3]     1.690294e-11
beta[4]     5.420895e-03
beta[5]     2.390562e-11
beta[6]     2.384583e-11
Name: params, dtype: float64, 'loglikelihood': 46.14064866845704, 'aic': -70.28129733691408, 'bic': np.float64(-63.251666711146235)}, 1960: {'params': mu          8.716877e-03
omega       4.045349e-07
alpha[1]    3.333409e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 78.39006151193601, 'aic': -134.78012302387202, 'bic': np.float64(-127.75049239810417)}, 1980: {'params': mu          0.020898
omega       0.000010
alpha[1]    0.066764
alpha[2]    0.066660
alpha[3]    0.066660
beta[1]     0.049995
beta[2]     0.049995
beta[3]     0.049995
beta[4]     0.049995
beta[5]     0.049995
beta[6]     0.049995
Name: params, dtype: float64, 'loglikelihood': 55.86225854841881, 'aic': -89.72451709683762, 'bic': np.float64(-82.69488647106976)}, 2000: {'params': mu          1.941324e-02
omega       8.650291e-07
alpha[1]    6.666671e-02
alpha[2]    6.666666e-02
alpha[3]    6.666666e-02
beta[1]     4.999999e-02
beta[2]     4.999999e-02
beta[3]     4.999999e-02
beta[4]     4.999999e-02
beta[5]     4.999999e-02
beta[6]     4.999999e-02
Name: params, dtype: float64, 'loglikelihood': 73.10743257542137, 'aic': -124.21486515084274, 'bic': np.float64(-117.18523452507489)}, 2020: {'params': mu          0.026804
omega       0.000023
alpha[1]    0.003337
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 50.18019374611075, 'aic': -78.3603874922215, 'bic': np.float64(-71.33075686645367)}, 2040: {'params': mu          0.032391
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 68.94335444983226, 'aic': -115.88670889966451, 'bic': np.float64(-108.85707827389666)}, 2060: {'params': mu          3.433720e-02
omega       6.351701e-07
alpha[1]    6.666666e-02
alpha[2]    6.666676e-02
alpha[3]    6.666666e-02
beta[1]     5.000000e-02
beta[2]     5.000000e-02
beta[3]     5.000000e-02
beta[4]     5.000000e-02
beta[5]     5.000000e-02
beta[6]     5.000000e-02
Name: params, dtype: float64, 'loglikelihood': 75.3951367494179, 'aic': -128.7902734988358, 'bic': np.float64(-121.76064287306795)}, 2080: {'params': mu          0.030058
omega       0.000021
alpha[1]    0.244481
alpha[2]    0.053425
alpha[3]    0.053425
beta[1]     0.040069
beta[2]     0.040069
beta[3]     0.040069
beta[4]     0.040069
beta[5]     0.040069
beta[6]     0.040069
Name: params, dtype: float64, 'loglikelihood': 50.47902603744999, 'aic': -78.95805207489998, 'bic': np.float64(-71.92842144913214)}, 2100: {'params': mu          0.039933
omega       0.000008
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 57.39551728486768, 'aic': -92.79103456973536, 'bic': np.float64(-85.76140394396751)}, 2120: {'params': mu          0.029997
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 67.62923173776717, 'aic': -113.25846347553434, 'bic': np.float64(-106.22883284976649)}, 2140: {'params': mu          0.035812
omega       0.000017
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003334
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 52.36677638732331, 'aic': -82.73355277464663, 'bic': np.float64(-75.70392214887877)}, 2160: {'params': mu          0.045054
omega       0.000009
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 56.96505259299462, 'aic': -91.93010518598923, 'bic': np.float64(-84.9004745602214)}, 2180: {'params': mu          0.043984
omega       0.000008
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 57.58288897243358, 'aic': -93.16577794486716, 'bic': np.float64(-86.13614731909931)}, 2200: {'params': mu          0.048509
omega       0.000005
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 61.16514802165488, 'aic': -100.33029604330976, 'bic': np.float64(-93.30066541754192)}, 2220: {'params': mu          0.076062
omega       0.000076
alpha[1]    0.003333
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beta[3]     0.081666
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beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 41.70460603898175, 'aic': -61.4092120779635, 'bic': np.float64(-54.37958145219566)}, 2240: {'params': mu          0.069042
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alpha[1]    0.003333
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beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 47.98307360781365, 'aic': -73.9661472156273, 'bic': np.float64(-66.93651658985945)}, 2260: {'params': mu          0.074282
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alpha[1]    0.066691
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beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 49.41404161643524, 'aic': -76.82808323287048, 'bic': np.float64(-69.79845260710263)}, 2280: {'params': mu          0.072834
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alpha[1]    0.003333
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beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 52.471515154622985, 'aic': -82.94303030924597, 'bic': np.float64(-75.91339968347813)}, 2300: {'params': mu          0.035640
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alpha[1]    0.209110
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alpha[3]    0.056512
beta[1]     0.042389
beta[2]     0.042389
beta[3]     0.042389
beta[4]     0.042389
beta[5]     0.042389
beta[6]     0.042389
Name: params, dtype: float64, 'loglikelihood': 47.41863365881509, 'aic': -72.83726731763018, 'bic': np.float64(-65.80763669186234)}, 2320: {'params': mu          0.042502
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beta[4]     0.039489
beta[5]     0.039489
beta[6]     0.039489
Name: params, dtype: float64, 'loglikelihood': 46.28862503532651, 'aic': -70.57725007065302, 'bic': np.float64(-63.54761944488518)}, 2340: {'params': mu          0.035465
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beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 61.15289706004869, 'aic': -100.30579412009737, 'bic': np.float64(-93.27616349432952)}, 2360: {'params': mu          4.182389e-02
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alpha[1]    9.999996e-01
alpha[2]    7.162136e-08
alpha[3]    7.163348e-08
beta[1]     5.374903e-08
beta[2]     5.378807e-08
beta[3]     5.380985e-08
beta[4]     5.386553e-08
beta[5]     5.383400e-08
beta[6]     5.368237e-08
Name: params, dtype: float64, 'loglikelihood': 40.42502043975818, 'aic': -58.85004087951636, 'bic': np.float64(-51.82041025374851)}, 2380: {'params': mu          0.048540
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alpha[1]    0.066691
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beta[1]     0.049999
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beta[4]     0.049999
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Name: params, dtype: float64, 'loglikelihood': 40.8553676752078, 'aic': -59.710735350415604, 'bic': np.float64(-52.68110472464776)}, 2400: {'params': mu          0.038417
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 55.24671105930972, 'aic': -88.49342211861943, 'bic': np.float64(-81.46379149285158)}, 2420: {'params': mu          0.063440
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beta[1]     0.081664
beta[2]     0.081664
beta[3]     0.081664
beta[4]     0.081664
beta[5]     0.081664
beta[6]     0.081664
Name: params, dtype: float64, 'loglikelihood': 36.44309503648478, 'aic': -50.886190072969555, 'bic': np.float64(-43.85655944720171)}, 2440: {'params': mu          0.035803
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beta[1]     0.042822
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beta[3]     0.042822
beta[4]     0.042822
beta[5]     0.042822
beta[6]     0.042822
Name: params, dtype: float64, 'loglikelihood': 42.042951254870125, 'aic': -62.08590250974025, 'bic': np.float64(-55.05627188397241)}, 2460: {'params': mu          0.051767
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alpha[1]    0.066680
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beta[5]     0.049999
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Name: params, dtype: float64, 'loglikelihood': 49.47480510434343, 'aic': -76.94961020868686, 'bic': np.float64(-69.91997958291901)}, 2480: {'params': mu          5.106599e-02
omega       9.641991e-07
alpha[1]    3.333333e-03
alpha[2]    3.333471e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
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beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 72.23549134229738, 'aic': -122.47098268459476, 'bic': np.float64(-115.44135205882691)}, 2500: {'params': mu          3.568163e-02
omega       2.016566e-05
alpha[1]    1.000000e+00
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alpha[3]    2.642708e-13
beta[1]     1.354457e-13
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beta[3]     4.463185e-13
beta[4]     6.027411e-13
beta[5]     7.239581e-13
beta[6]     7.795125e-13
Name: params, dtype: float64, 'loglikelihood': 48.845331928088704, 'aic': -75.69066385617741, 'bic': np.float64(-68.66103323040957)}, 2520: {'params': mu          0.012861
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alpha[1]    0.066687
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beta[1]     0.049999
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beta[4]     0.049999
beta[5]     0.049999
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Name: params, dtype: float64, 'loglikelihood': 63.550248414606855, 'aic': -105.10049682921371, 'bic': np.float64(-98.07086620344586)}, 2540: {'params': mu          0.045251
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alpha[1]    1.000000
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beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 42.97539036543505, 'aic': -63.95078073087009, 'bic': np.float64(-56.92115010510225)}, 2560: {'params': mu          0.042513
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alpha[1]    0.144339
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alpha[3]    0.061118
beta[1]     0.045839
beta[2]     0.045839
beta[3]     0.045839
beta[4]     0.045839
beta[5]     0.045839
beta[6]     0.045839
Name: params, dtype: float64, 'loglikelihood': 45.75180116868323, 'aic': -69.50360233736646, 'bic': np.float64(-62.473971711598615)}, 2580: {'params': mu          0.021787
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alpha[1]    0.033334
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beta[1]     0.066667
beta[2]     0.066667
beta[3]     0.066667
beta[4]     0.066667
beta[5]     0.066667
beta[6]     0.066667
Name: params, dtype: float64, 'loglikelihood': 55.96314638508649, 'aic': -89.92629277017298, 'bic': np.float64(-82.89666214440513)}, 2600: {'params': mu          1.857786e-02
omega       6.943360e-06
alpha[1]    9.999932e-01
alpha[2]    8.692604e-07
alpha[3]    8.693095e-07
beta[1]     6.519656e-07
beta[2]     6.520019e-07
beta[3]     6.520406e-07
beta[4]     6.520473e-07
beta[5]     6.520613e-07
beta[6]     6.520741e-07
Name: params, dtype: float64, 'loglikelihood': 56.46914551582993, 'aic': -90.93829103165986, 'bic': np.float64(-83.90866040589202)}, 2620: {'params': mu          0.065881
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
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beta[4]     0.050000
beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 50.30569820535635, 'aic': -78.6113964107127, 'bic': np.float64(-71.58176578494485)}, 2640: {'params': mu          0.020888
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alpha[1]    0.305658
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beta[3]     0.033343
beta[4]     0.033343
beta[5]     0.033343
beta[6]     0.033343
Name: params, dtype: float64, 'loglikelihood': 50.987902477089534, 'aic': -79.97580495417907, 'bic': np.float64(-72.94617432841122)}, 2660: {'params': mu          1.209997e-02
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alpha[1]    3.333560e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     1.150000e-01
beta[2]     1.150000e-01
beta[3]     1.150000e-01
beta[4]     1.150000e-01
beta[5]     1.150000e-01
beta[6]     1.150000e-01
Name: params, dtype: float64, 'loglikelihood': 68.50628189056256, 'aic': -115.01256378112512, 'bic': np.float64(-107.98293315535727)}, 2680: {'params': mu          0.022348
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alpha[1]    0.066670
alpha[2]    0.066666
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beta[4]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 52.46089426068031, 'aic': -82.92178852136063, 'bic': np.float64(-75.89215789559279)}, 2700: {'params': mu          0.014500
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alpha[1]    0.066669
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beta[4]     0.050000
beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 61.258593705949636, 'aic': -100.51718741189927, 'bic': np.float64(-93.48755678613142)}, 2720: {'params': mu          0.006825
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 67.96651933673525, 'aic': -113.93303867347049, 'bic': np.float64(-106.90340804770264)}, 2740: {'params': mu          0.013331
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 65.51830572004337, 'aic': -109.03661144008674, 'bic': np.float64(-102.0069808143189)}, 2760: {'params': mu          0.011125
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alpha[1]    0.066667
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beta[3]     0.050000
beta[4]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 69.29022992638521, 'aic': -116.58045985277042, 'bic': np.float64(-109.55082922700257)}, 2780: {'params': mu          0.058710
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alpha[1]    0.999999
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beta[3]     0.000013
beta[4]     0.000013
beta[5]     0.000013
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Name: params, dtype: float64, 'loglikelihood': 47.68863079672328, 'aic': -73.37726159344656, 'bic': np.float64(-66.34763096767873)}, 2800: {'params': mu          0.025611
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alpha[1]    0.066710
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beta[1]     0.049998
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beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 50.65509015562267, 'aic': -79.31018031124535, 'bic': np.float64(-72.2805496854775)}, 2820: {'params': mu          0.058671
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alpha[1]    0.568473
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beta[4]     0.023129
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Name: params, dtype: float64, 'loglikelihood': 57.4223737793823, 'aic': -92.8447475587646, 'bic': np.float64(-85.81511693299674)}, 2840: {'params': mu          0.029152
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alpha[1]    0.066666
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Name: params, dtype: float64, 'loglikelihood': 59.89808180993005, 'aic': -97.7961636198601, 'bic': np.float64(-90.76653299409224)}, 2860: {'params': mu          1.116960e-02
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alpha[1]    6.666682e-02
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beta[3]     4.999999e-02
beta[4]     4.999999e-02
beta[5]     4.999999e-02
beta[6]     4.999999e-02
Name: params, dtype: float64, 'loglikelihood': 72.02063779699729, 'aic': -122.04127559399458, 'bic': np.float64(-115.01164496822673)}, 2880: {'params': mu          0.014234
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beta[5]     0.049998
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Name: params, dtype: float64, 'loglikelihood': 58.47760303700191, 'aic': -94.95520607400383, 'bic': np.float64(-87.92557544823597)}, 2900: {'params': mu          0.007424
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alpha[1]    0.066667
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beta[4]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 68.87594788554696, 'aic': -115.75189577109393, 'bic': np.float64(-108.72226514532608)}, 2920: {'params': mu          0.012377
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alpha[1]    0.068855
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beta[4]     0.049874
beta[5]     0.049874
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Name: params, dtype: float64, 'loglikelihood': 64.35815725717708, 'aic': -106.71631451435417, 'bic': np.float64(-99.68668388858632)}, 2940: {'params': mu          0.019563
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alpha[1]    0.066667
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Name: params, dtype: float64, 'loglikelihood': 67.98944251272758, 'aic': -113.97888502545516, 'bic': np.float64(-106.9492543996873)}, 2960: {'params': mu          0.024016
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alpha[1]    0.066666
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Name: params, dtype: float64, 'loglikelihood': 57.233607264643325, 'aic': -92.46721452928665, 'bic': np.float64(-85.4375839035188)}, 2980: {'params': mu          5.273624e-02
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beta[4]     0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 46.448195508994026, 'aic': -70.89639101798805, 'bic': np.float64(-63.86676039222021)}, 3000: {'params': mu          0.029867
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Name: params, dtype: float64, 'loglikelihood': 64.8750192661594, 'aic': -107.7500385323188, 'bic': np.float64(-100.72040790655095)}, 3020: {'params': mu          0.031085
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
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Name: params, dtype: float64, 'loglikelihood': 67.04756568522235, 'aic': -112.0951313704447, 'bic': np.float64(-105.06550074467685)}, 3040: {'params': mu          0.055205
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beta[4]     0.031884
beta[5]     0.031884
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Name: params, dtype: float64, 'loglikelihood': 42.84225882177782, 'aic': -63.68451764355564, 'bic': np.float64(-56.65488701778779)}, 3060: {'params': mu          0.027608
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beta[3]     0.045013
beta[4]     0.045013
beta[5]     0.045013
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Name: params, dtype: float64, 'loglikelihood': 43.81322662213564, 'aic': -65.62645324427127, 'bic': np.float64(-58.59682261850343)}, 3080: {'params': mu          0.011247
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alpha[1]    0.066667
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alpha[3]    0.066667
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beta[4]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 69.66464189588567, 'aic': -117.32928379177133, 'bic': np.float64(-110.29965316600348)}, 3100: {'params': mu          0.013533
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
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Name: params, dtype: float64, 'loglikelihood': 48.475954159094215, 'aic': -74.95190831818843, 'bic': np.float64(-67.92227769242058)}, 3140: {'params': mu          0.021943
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Name: params, dtype: float64, 'loglikelihood': 54.48392306864286, 'aic': -86.96784613728572, 'bic': np.float64(-79.93821551151788)}, 3160: {'params': mu          0.028349
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Name: params, dtype: float64, 'loglikelihood': 50.48810723296353, 'aic': -78.97621446592706, 'bic': np.float64(-71.9465838401592)}, 3180: {'params': mu          1.900697e-02
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beta[1]     8.166666e-02
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beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
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Name: params, dtype: float64, 'loglikelihood': 73.83477312246596, 'aic': -125.66954624493192, 'bic': np.float64(-118.63991561916407)}, 3200: {'params': mu          0.013054
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alpha[1]    0.003333
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Name: params, dtype: float64, 'loglikelihood': 65.7025630504675, 'aic': -109.40512610093501, 'bic': np.float64(-102.37549547516716)}, 3220: {'params': mu          0.011240
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Name: params, dtype: float64, 'loglikelihood': 66.88697121852877, 'aic': -111.77394243705754, 'bic': np.float64(-104.74431181128969)}, 3240: {'params': mu          0.024264
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Name: params, dtype: float64, 'loglikelihood': 71.77652789054257, 'aic': -121.55305578108513, 'bic': np.float64(-114.52342515531728)}, 3260: {'params': mu          0.022936
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
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Name: params, dtype: float64, 'loglikelihood': 68.88156908341072, 'aic': -115.76313816682145, 'bic': np.float64(-108.7335075410536)}, 3280: {'params': mu          0.038066
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beta[3]     0.050000
beta[4]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 61.110593680916566, 'aic': -100.22118736183313, 'bic': np.float64(-93.19155673606528)}, 3300: {'params': mu          0.029402
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Name: params, dtype: float64, 'loglikelihood': 53.961394844675574, 'aic': -85.92278968935115, 'bic': np.float64(-78.89315906358331)}, 3320: {'params': mu          0.043782
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Name: params, dtype: float64, 'loglikelihood': 53.05619606734739, 'aic': -84.11239213469479, 'bic': np.float64(-77.08276150892695)}, 3340: {'params': mu          1.282586e-01
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beta[4]     1.110076e-07
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Name: params, dtype: float64, 'loglikelihood': 37.52828576665604, 'aic': -53.05657153331208, 'bic': np.float64(-46.02694090754424)}, 3360: {'params': mu          0.036012
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Name: params, dtype: float64, 'loglikelihood': 50.47752792162602, 'aic': -78.95505584325204, 'bic': np.float64(-71.92542521748419)}, 3380: {'params': mu          0.019148
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Name: params, dtype: float64, 'loglikelihood': 60.80309966756394, 'aic': -99.60619933512788, 'bic': np.float64(-92.57656870936003)}, 3400: {'params': mu          0.055772
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Name: params, dtype: float64, 'loglikelihood': 44.91585092041514, 'aic': -67.83170184083028, 'bic': np.float64(-60.80207121506243)}, 3420: {'params': mu          0.026641
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Name: params, dtype: float64, 'loglikelihood': 53.706979574992495, 'aic': -85.41395914998499, 'bic': np.float64(-78.38432852421715)}, 3440: {'params': mu          0.032190
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beta[3]     0.049995
beta[4]     0.049995
beta[5]     0.049995
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Name: params, dtype: float64, 'loglikelihood': 51.784367146533135, 'aic': -81.56873429306627, 'bic': np.float64(-74.53910366729843)}, 3460: {'params': mu          0.037422
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beta[3]     0.049981
beta[4]     0.049981
beta[5]     0.049981
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Name: params, dtype: float64, 'loglikelihood': 57.87425997384776, 'aic': -93.74851994769551, 'bic': np.float64(-86.71888932192766)}, 3480: {'params': mu          0.019613
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Name: params, dtype: float64, 'loglikelihood': 55.48455678614617, 'aic': -88.96911357229234, 'bic': np.float64(-81.93948294652449)}, 3500: {'params': mu          4.032827e-02
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beta[4]     2.676818e-07
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Name: params, dtype: float64, 'loglikelihood': 46.65239551722602, 'aic': -71.30479103445204, 'bic': np.float64(-64.2751604086842)}, 3520: {'params': mu          0.014151
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Name: params, dtype: float64, 'loglikelihood': 59.88551850206827, 'aic': -97.77103700413655, 'bic': np.float64(-90.74140637836871)}, 3540: {'params': mu          0.020996
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Name: params, dtype: float64, 'loglikelihood': 60.14163434841519, 'aic': -98.28326869683038, 'bic': np.float64(-91.25363807106254)}, 3560: {'params': mu          0.030030
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beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 62.541352750096394, 'aic': -103.08270550019279, 'bic': np.float64(-96.05307487442494)}, 3580: {'params': mu          0.034061
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
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Name: params, dtype: float64, 'loglikelihood': 63.279612869720395, 'aic': -104.55922573944079, 'bic': np.float64(-97.52959511367294)}, 3600: {'params': mu          0.023489
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Name: params, dtype: float64, 'loglikelihood': 60.65838669306986, 'aic': -99.31677338613972, 'bic': np.float64(-92.28714276037186)}, 3620: {'params': mu          0.073898
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Name: params, dtype: float64, 'loglikelihood': 47.41174673532913, 'aic': -72.82349347065826, 'bic': np.float64(-65.79386284489041)}, 3640: {'params': mu          0.071745
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Name: params, dtype: float64, 'loglikelihood': 38.72208500470632, 'aic': -55.444170009412645, 'bic': np.float64(-48.4145393836448)}, 3660: {'params': mu          9.432426e-02
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Name: params, dtype: float64, 'loglikelihood': 7.641748710123428, 'aic': 6.7165025797531435, 'bic': np.float64(13.746133205520987)}, 3680: {'params': mu          7.467694e-02
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Name: params, dtype: float64, 'loglikelihood': 20.37121423664781, 'aic': -18.742428473295618, 'bic': np.float64(-11.712797847527774)}, 3700: {'params': mu          0.031079
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Name: params, dtype: float64, 'loglikelihood': 68.35009509955711, 'aic': -114.70019019911422, 'bic': np.float64(-107.67055957334637)}, 3720: {'params': mu          0.057585
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Name: params, dtype: float64, 'loglikelihood': 51.565451381191366, 'aic': -81.13090276238273, 'bic': np.float64(-74.10127213661488)}, 3740: {'params': mu          0.145133
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Name: params, dtype: float64, 'loglikelihood': 43.609849098900426, 'aic': -65.21969819780085, 'bic': np.float64(-58.19006757203301)}, 3760: {'params': mu          0.120806
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Name: params, dtype: float64, 'loglikelihood': 42.67509982001158, 'aic': -63.35019964002316, 'bic': np.float64(-56.32056901425532)}, 3780: {'params': mu          0.059196
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Name: params, dtype: float64, 'loglikelihood': 58.28719397292486, 'aic': -94.57438794584972, 'bic': np.float64(-87.54475732008189)}, 3800: {'params': mu          0.031557
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Name: params, dtype: float64, 'loglikelihood': 42.32292187223478, 'aic': -62.64584374446956, 'bic': np.float64(-55.616213118701715)}, 3820: {'params': mu          0.030114
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Name: params, dtype: float64, 'loglikelihood': 39.3499898329745, 'aic': -56.699979665949, 'bic': np.float64(-49.67034904018116)}, 3840: {'params': mu          0.044632
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Name: params, dtype: float64, 'loglikelihood': 60.92095328492827, 'aic': -99.84190656985653, 'bic': np.float64(-92.8122759440887)}, 3860: {'params': mu          0.021953
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Name: params, dtype: float64, 'loglikelihood': 56.32994133650597, 'aic': -90.65988267301194, 'bic': np.float64(-83.63025204724408)}, 3880: {'params': mu          0.028334
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Name: params, dtype: float64, 'loglikelihood': 52.95572678815506, 'aic': -83.91145357631012, 'bic': np.float64(-76.88182295054227)}, 3900: {'params': mu          0.076753
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Name: params, dtype: float64, 'loglikelihood': 46.00388916504045, 'aic': -70.0077783300809, 'bic': np.float64(-62.97814770431305)}, 3920: {'params': mu          0.033846
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Name: params, dtype: float64, 'loglikelihood': 55.294581721538485, 'aic': -88.58916344307697, 'bic': np.float64(-81.55953281730913)}, 3940: {'params': mu          0.025402
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Name: params, dtype: float64, 'loglikelihood': 57.882296182339815, 'aic': -93.76459236467963, 'bic': np.float64(-86.73496173891178)}, 3960: {'params': mu          0.077778
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Name: params, dtype: float64, 'loglikelihood': 26.482437309954975, 'aic': -30.96487461990995, 'bic': np.float64(-23.935243994142105)}, 4000: {'params': mu          0.061483
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Name: params, dtype: float64, 'loglikelihood': 51.25414502438659, 'aic': -80.50829004877318, 'bic': np.float64(-73.47865942300533)}, 4240: {'params': mu          0.028776
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Name: params, dtype: float64, 'loglikelihood': 56.403744356103466, 'aic': -90.80748871220693, 'bic': np.float64(-83.7778580864391)}, 4300: {'params': mu          0.015846
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Name: params, dtype: float64, 'loglikelihood': 61.03828520497264, 'aic': -100.07657040994528, 'bic': np.float64(-93.04693978417743)}, 4340: {'params': mu          0.019907
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Name: params, dtype: float64, 'loglikelihood': 104.0089397137036, 'aic': -186.0178794274072, 'bic': np.float64(-171.36362981547995)}, 860: {'params': mu          0.029739
omega       0.000006
alpha[1]    0.016667
alpha[2]    0.016667
alpha[3]    0.016667
beta[1]     0.075000
beta[2]     0.075000
beta[3]     0.075000
beta[4]     0.075000
beta[5]     0.075000
beta[6]     0.075000
Name: params, dtype: float64, 'loglikelihood': 119.04957497672677, 'aic': -216.09914995345355, 'bic': np.float64(-201.4449003415263)}, 880: {'params': mu          0.035324
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alpha[1]    0.066685
alpha[2]    0.066665
alpha[3]    0.066665
beta[1]     0.049999
beta[2]     0.049999
beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 105.27957402751933, 'aic': -188.55914805503866, 'bic': np.float64(-173.90489844311142)}, 900: {'params': mu          0.042588
omega       0.000006
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 120.33662274005653, 'aic': -218.67324548011305, 'bic': np.float64(-204.0189958681858)}, 920: {'params': mu          0.034002
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 107.58113529571341, 'aic': -193.16227059142682, 'bic': np.float64(-178.50802097949958)}, 940: {'params': mu          0.033932
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alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 141.21625238978183, 'aic': -260.43250477956366, 'bic': np.float64(-245.77825516763642)}, 960: {'params': mu          0.030665
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alpha[1]    0.069856
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alpha[3]    0.066439
beta[1]     0.049829
beta[2]     0.049829
beta[3]     0.049829
beta[4]     0.049829
beta[5]     0.049829
beta[6]     0.049829
Name: params, dtype: float64, 'loglikelihood': 110.57971731648783, 'aic': -199.15943463297566, 'bic': np.float64(-184.50518502104842)}, 980: {'params': mu          0.045994
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alpha[1]    0.066685
alpha[2]    0.066665
alpha[3]    0.066665
beta[1]     0.049999
beta[2]     0.049999
beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 82.6041937331183, 'aic': -143.2083874662366, 'bic': np.float64(-128.55413785430935)}, 1000: {'params': mu          0.053830
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alpha[1]    0.066669
alpha[2]    0.066666
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beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 103.93033295708929, 'aic': -185.86066591417858, 'bic': np.float64(-171.20641630225134)}, 1020: {'params': mu          5.906502e-02
omega       1.415293e-08
alpha[1]    6.373479e-01
alpha[2]    9.859596e-04
alpha[3]    9.859620e-04
beta[1]     7.394679e-04
beta[2]     7.394703e-04
beta[3]     7.394693e-04
beta[4]     7.394623e-04
beta[5]     7.394654e-04
beta[6]     2.967242e-01
Name: params, dtype: float64, 'loglikelihood': 86.75071551442336, 'aic': -151.50143102884672, 'bic': np.float64(-136.84718141691948)}, 1040: {'params': mu          0.042796
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.06866313176735, 'aic': -174.1373262635347, 'bic': np.float64(-159.48307665160746)}, 1060: {'params': mu          0.029316
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 108.79080012742472, 'aic': -195.58160025484943, 'bic': np.float64(-180.9273506429222)}, 1080: {'params': mu          0.033840
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 116.1324722144856, 'aic': -210.2649444289712, 'bic': np.float64(-195.61069481704396)}, 1100: {'params': mu          0.044386
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alpha[1]    0.066672
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alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.70917602006539, 'aic': -175.41835204013077, 'bic': np.float64(-160.76410242820353)}, 1120: {'params': mu          0.049939
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alpha[1]    0.068340
alpha[2]    0.066547
alpha[3]    0.066547
beta[1]     0.083184
beta[2]     0.083184
beta[3]     0.083184
beta[4]     0.083184
beta[5]     0.083184
beta[6]     0.083184
Name: params, dtype: float64, 'loglikelihood': 108.28162590942908, 'aic': -194.56325181885816, 'bic': np.float64(-179.90900220693092)}, 1140: {'params': mu          0.055105
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 105.67071347240598, 'aic': -189.34142694481196, 'bic': np.float64(-174.68717733288472)}, 1160: {'params': mu          0.037858
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alpha[1]    0.067703
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alpha[3]    0.066593
beta[1]     0.049944
beta[2]     0.049944
beta[3]     0.049944
beta[4]     0.049944
beta[5]     0.049944
beta[6]     0.049944
Name: params, dtype: float64, 'loglikelihood': 93.0968102386939, 'aic': -164.1936204773878, 'bic': np.float64(-149.53937086546057)}, 1180: {'params': mu          0.035649
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alpha[1]    0.066671
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alpha[3]    0.066666
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 113.70278353514043, 'aic': -205.40556707028085, 'bic': np.float64(-190.7513174583536)}, 1200: {'params': mu          0.036211
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 102.28639791921906, 'aic': -182.5727958384381, 'bic': np.float64(-167.91854622651087)}, 1220: {'params': mu          0.028502
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
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beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 104.63211984430342, 'aic': -187.26423968860684, 'bic': np.float64(-172.6099900766796)}, 1240: {'params': mu          0.016227
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alpha[1]    0.066672
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 112.14001686496643, 'aic': -202.28003372993285, 'bic': np.float64(-187.6257841180056)}, 1260: {'params': mu          0.020689
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alpha[1]    0.066668
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 99.67931411255594, 'aic': -177.3586282251119, 'bic': np.float64(-162.70437861318464)}, 1280: {'params': mu          0.029150
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alpha[1]    0.066665
alpha[2]    0.066665
alpha[3]    0.066665
beta[1]     0.083331
beta[2]     0.083331
beta[3]     0.083331
beta[4]     0.083331
beta[5]     0.083331
beta[6]     0.083331
Name: params, dtype: float64, 'loglikelihood': 87.57622227649733, 'aic': -153.15244455299467, 'bic': np.float64(-138.49819494106742)}, 1300: {'params': mu          0.023450
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alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 103.32647636281105, 'aic': -184.6529527256221, 'bic': np.float64(-169.99870311369486)}, 1320: {'params': mu          0.027777
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alpha[1]    0.435337
alpha[2]    0.040333
alpha[3]    0.040333
beta[1]     0.030250
beta[2]     0.030250
beta[3]     0.030250
beta[4]     0.030250
beta[5]     0.030250
beta[6]     0.030250
Name: params, dtype: float64, 'loglikelihood': 88.8624224056158, 'aic': -155.7248448112316, 'bic': np.float64(-141.07059519930436)}, 1340: {'params': mu          0.014223
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 128.7998301673174, 'aic': -235.5996603346348, 'bic': np.float64(-220.94541072270755)}, 1360: {'params': mu          0.022645
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alpha[1]    0.066672
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.1795413182273, 'aic': -174.3590826364546, 'bic': np.float64(-159.70483302452735)}, 1380: {'params': mu          0.035681
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alpha[1]    0.200262
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alpha[3]    0.057124
beta[1]     0.071405
beta[2]     0.071405
beta[3]     0.071405
beta[4]     0.071405
beta[5]     0.071405
beta[6]     0.071405
Name: params, dtype: float64, 'loglikelihood': 113.01674601715393, 'aic': -204.03349203430787, 'bic': np.float64(-189.37924242238063)}, 1400: {'params': mu          0.040047
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alpha[1]    0.003334
alpha[2]    0.003333
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beta[1]     0.115000
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beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 106.2605670614907, 'aic': -190.5211341229814, 'bic': np.float64(-175.86688451105417)}, 1420: {'params': mu          0.034837
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alpha[1]    0.077359
alpha[2]    0.065903
alpha[3]    0.065903
beta[1]     0.049427
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beta[3]     0.049427
beta[4]     0.049427
beta[5]     0.049427
beta[6]     0.049427
Name: params, dtype: float64, 'loglikelihood': 115.84358207290215, 'aic': -209.6871641458043, 'bic': np.float64(-195.03291453387706)}, 1440: {'params': mu          0.040759
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alpha[1]    0.991480
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alpha[3]    0.000020
beta[1]     0.000025
beta[2]     0.000025
beta[3]     0.000025
beta[4]     0.000025
beta[5]     0.006478
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Name: params, dtype: float64, 'loglikelihood': 57.36125759334167, 'aic': -92.72251518668334, 'bic': np.float64(-78.0682655747561)}, 1460: {'params': mu          0.030591
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alpha[1]    0.986820
alpha[2]    0.005082
alpha[3]    0.002383
beta[1]     0.000984
beta[2]     0.000776
beta[3]     0.000634
beta[4]     0.000437
beta[5]     0.000363
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Name: params, dtype: float64, 'loglikelihood': 51.31509134491049, 'aic': -80.63018268982098, 'bic': np.float64(-65.97593307789374)}, 1480: {'params': mu          0.027093
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 116.567700842078, 'aic': -211.135401684156, 'bic': np.float64(-196.48115207222875)}, 1500: {'params': mu          0.024244
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alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 118.05135323531178, 'aic': -214.10270647062356, 'bic': np.float64(-199.44845685869632)}, 1520: {'params': mu          0.029009
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alpha[1]    0.066691
alpha[2]    0.066665
alpha[3]    0.066665
beta[1]     0.083331
beta[2]     0.083331
beta[3]     0.083331
beta[4]     0.083331
beta[5]     0.083331
beta[6]     0.083331
Name: params, dtype: float64, 'loglikelihood': 111.14056262499301, 'aic': -200.28112524998602, 'bic': np.float64(-185.62687563805878)}, 1540: {'params': mu          0.026009
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alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.16594061047296, 'aic': -174.33188122094592, 'bic': np.float64(-159.67763160901868)}, 1560: {'params': mu          0.025722
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 103.22756657856908, 'aic': -184.45513315713816, 'bic': np.float64(-169.80088354521092)}, 1580: {'params': mu          0.025620
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alpha[1]    0.120546
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alpha[3]    0.062818
beta[1]     0.078523
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beta[3]     0.078523
beta[4]     0.078523
beta[5]     0.078523
beta[6]     0.078523
Name: params, dtype: float64, 'loglikelihood': 86.11281210962088, 'aic': -150.22562421924175, 'bic': np.float64(-135.5713746073145)}, 1600: {'params': mu          0.029840
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alpha[1]    0.220263
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beta[2]     0.040499
beta[3]     0.040499
beta[4]     0.040499
beta[5]     0.040499
beta[6]     0.040499
Name: params, dtype: float64, 'loglikelihood': 81.69739697732052, 'aic': -141.39479395464105, 'bic': np.float64(-126.7405443427138)}, 1620: {'params': mu          2.724073e-02
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alpha[2]    2.423181e-08
alpha[3]    0.000000e+00
beta[1]     2.478342e-08
beta[2]     1.115637e-08
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beta[4]     1.115407e-08
beta[5]     1.115466e-08
beta[6]     3.427364e-08
Name: params, dtype: float64, 'loglikelihood': 90.10201274347916, 'aic': -158.20402548695833, 'bic': np.float64(-143.5497758750311)}, 1640: {'params': mu          0.024298
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alpha[1]    0.066670
alpha[2]    0.066666
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 95.04345341959238, 'aic': -168.08690683918476, 'bic': np.float64(-153.43265722725752)}, 1660: {'params': mu          0.035673
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alpha[1]    0.066670
alpha[2]    0.066666
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 106.38598840968929, 'aic': -190.77197681937858, 'bic': np.float64(-176.11772720745134)}, 1680: {'params': mu          0.037843
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alpha[1]    0.248271
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alpha[3]    0.049494
beta[1]     0.086614
beta[2]     0.086614
beta[3]     0.086614
beta[4]     0.086614
beta[5]     0.086615
beta[6]     0.086615
Name: params, dtype: float64, 'loglikelihood': 86.88183419301333, 'aic': -151.76366838602667, 'bic': np.float64(-137.10941877409942)}, 1700: {'params': mu          0.065995
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alpha[1]    0.066846
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beta[2]     0.049990
beta[3]     0.049990
beta[4]     0.049990
beta[5]     0.049990
beta[6]     0.049990
Name: params, dtype: float64, 'loglikelihood': 98.35805457639745, 'aic': -174.7161091527949, 'bic': np.float64(-160.06185954086766)}, 1720: {'params': mu          0.027274
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alpha[1]    0.992223
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beta[3]     0.000417
beta[4]     0.000417
beta[5]     0.000417
beta[6]     0.000417
Name: params, dtype: float64, 'loglikelihood': 79.8199450366027, 'aic': -137.6398900732054, 'bic': np.float64(-122.98564046127817)}, 1740: {'params': mu          0.037754
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alpha[1]    0.066671
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beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 96.89969168295967, 'aic': -171.79938336591934, 'bic': np.float64(-157.1451337539921)}, 1760: {'params': mu          0.044760
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alpha[1]    0.244018
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beta[3]     0.040499
beta[4]     0.040499
beta[5]     0.040499
beta[6]     0.040499
Name: params, dtype: float64, 'loglikelihood': 82.04222009038897, 'aic': -142.08444018077793, 'bic': np.float64(-127.43019056885069)}, 1780: {'params': mu          0.021702
omega       0.000019
alpha[1]    0.070822
alpha[2]    0.066370
alpha[3]    0.066370
beta[1]     0.082963
beta[2]     0.082963
beta[3]     0.082963
beta[4]     0.082963
beta[5]     0.082963
beta[6]     0.082963
Name: params, dtype: float64, 'loglikelihood': 101.4548283943664, 'aic': -180.9096567887328, 'bic': np.float64(-166.25540717680556)}, 1800: {'params': mu          0.033949
omega       0.000047
alpha[1]    0.802625
alpha[2]    0.000006
alpha[3]    0.000006
beta[1]     0.000008
beta[2]     0.000008
beta[3]     0.000008
beta[4]     0.000008
beta[5]     0.000008
beta[6]     0.000008
Name: params, dtype: float64, 'loglikelihood': 82.52801985319688, 'aic': -143.05603970639376, 'bic': np.float64(-128.40179009446652)}, 1820: {'params': mu          0.013641
omega       0.000021
alpha[1]    0.066871
alpha[2]    0.066652
alpha[3]    0.066652
beta[1]     0.083315
beta[2]     0.083315
beta[3]     0.083315
beta[4]     0.083315
beta[5]     0.083315
beta[6]     0.083315
Name: params, dtype: float64, 'loglikelihood': 98.16815914463042, 'aic': -174.33631828926084, 'bic': np.float64(-159.6820686773336)}, 1840: {'params': mu          0.026630
omega       0.000022
alpha[1]    0.070159
alpha[2]    0.066417
alpha[3]    0.066417
beta[1]     0.049813
beta[2]     0.049813
beta[3]     0.049813
beta[4]     0.049813
beta[5]     0.049813
beta[6]     0.049813
Name: params, dtype: float64, 'loglikelihood': 101.16996313430613, 'aic': -180.33992626861226, 'bic': np.float64(-165.68567665668502)}, 1860: {'params': mu          0.019333
omega       0.000008
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 108.00599184588621, 'aic': -194.01198369177243, 'bic': np.float64(-179.3577340798452)}, 1880: {'params': mu          0.034548
omega       0.000037
alpha[1]    0.066772
alpha[2]    0.066659
alpha[3]    0.066659
beta[1]     0.049994
beta[2]     0.049994
beta[3]     0.049994
beta[4]     0.049994
beta[5]     0.049994
beta[6]     0.049994
Name: params, dtype: float64, 'loglikelihood': 96.48286441054661, 'aic': -170.96572882109322, 'bic': np.float64(-156.31147920916598)}, 1900: {'params': mu          0.042088
omega       0.000014
alpha[1]    0.173626
alpha[2]    0.059027
alpha[3]    0.059027
beta[1]     0.044270
beta[2]     0.044270
beta[3]     0.044270
beta[4]     0.044270
beta[5]     0.044270
beta[6]     0.044270
Name: params, dtype: float64, 'loglikelihood': 106.44035272802448, 'aic': -190.88070545604896, 'bic': np.float64(-176.22645584412172)}, 1920: {'params': mu          0.051846
omega       0.000065
alpha[1]    0.192768
alpha[2]    0.057594
alpha[3]    0.057594
beta[1]     0.043195
beta[2]     0.043195
beta[3]     0.043195
beta[4]     0.043195
beta[5]     0.043195
beta[6]     0.043195
Name: params, dtype: float64, 'loglikelihood': 86.26981512074002, 'aic': -150.53963024148004, 'bic': np.float64(-135.8853806295528)}, 1940: {'params': mu          9.732524e-03
omega       1.361715e-05
alpha[1]    9.999995e-01
alpha[2]    1.007342e-11
alpha[3]    2.781322e-11
beta[1]     1.853874e-11
beta[2]     3.627785e-11
beta[3]     6.299125e-11
beta[4]     8.874408e-11
beta[5]     1.208825e-10
beta[6]     1.729882e-10
Name: params, dtype: float64, 'loglikelihood': 76.40011318226551, 'aic': -130.80022636453103, 'bic': np.float64(-116.14597675260379)}, 1960: {'params': mu          0.012558
omega       0.000021
alpha[1]    0.192594
alpha[2]    0.057672
alpha[3]    0.057672
beta[1]     0.043254
beta[2]     0.043254
beta[3]     0.043254
beta[4]     0.043254
beta[5]     0.043254
beta[6]     0.043254
Name: params, dtype: float64, 'loglikelihood': 100.73194617389261, 'aic': -179.46389234778522, 'bic': np.float64(-164.80964273585798)}, 1980: {'params': mu          0.019126
omega       0.000008
alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 115.0229964222232, 'aic': -208.0459928444464, 'bic': np.float64(-193.39174323251916)}, 2000: {'params': mu          0.025756
omega       0.000020
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 101.72234384468065, 'aic': -181.4446876893613, 'bic': np.float64(-166.79043807743406)}, 2020: {'params': mu          2.809377e-02
omega       2.241090e-05
alpha[1]    3.472784e-01
alpha[2]    0.000000e+00
alpha[3]    1.342213e-13
beta[1]     4.284805e-13
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 104.5353668624053, 'aic': -187.0707337248106, 'bic': np.float64(-172.41648411288335)}, 2040: {'params': mu          0.033011
omega       0.000004
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 124.78468253093978, 'aic': -227.56936506187955, 'bic': np.float64(-212.9151154499523)}, 2060: {'params': mu          0.031976
omega       0.000009
alpha[1]    0.071279
alpha[2]    0.066370
alpha[3]    0.066370
beta[1]     0.049778
beta[2]     0.049778
beta[3]     0.049778
beta[4]     0.049778
beta[5]     0.049778
beta[6]     0.049778
Name: params, dtype: float64, 'loglikelihood': 114.92575077000811, 'aic': -207.85150154001622, 'bic': np.float64(-193.19725192808897)}, 2080: {'params': mu          0.037718
omega       0.000026
alpha[1]    0.066671
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 99.66132640356092, 'aic': -177.32265280712184, 'bic': np.float64(-162.6684031951946)}, 2100: {'params': mu          0.033418
omega       0.000029
alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 97.51840834738445, 'aic': -173.0368166947689, 'bic': np.float64(-158.38256708284166)}, 2120: {'params': mu          0.029905
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 129.09600441534033, 'aic': -236.19200883068066, 'bic': np.float64(-221.53775921875342)}, 2140: {'params': mu          0.040612
omega       0.000016
alpha[1]    0.066668
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 106.86427880830524, 'aic': -191.7285576166105, 'bic': np.float64(-177.07430800468325)}, 2160: {'params': mu          0.045410
omega       0.000004
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 119.7559978431909, 'aic': -217.5119956863818, 'bic': np.float64(-202.85774607445455)}, 2180: {'params': mu          0.047379
omega       0.000007
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 109.43032562751345, 'aic': -196.8606512550269, 'bic': np.float64(-182.20640164309967)}, 2200: {'params': mu          0.052210
omega       0.000042
alpha[1]    0.265130
alpha[2]    0.052491
alpha[3]    0.052491
beta[1]     0.039368
beta[2]     0.039368
beta[3]     0.039368
beta[4]     0.039368
beta[5]     0.039368
beta[6]     0.039368
Name: params, dtype: float64, 'loglikelihood': 92.55008462080507, 'aic': -163.10016924161013, 'bic': np.float64(-148.4459196296829)}, 2220: {'params': mu          0.073373
omega       0.000039
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.114999
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beta[3]     0.114999
beta[4]     0.114999
beta[5]     0.114999
beta[6]     0.114999
Name: params, dtype: float64, 'loglikelihood': 85.42425386815104, 'aic': -148.84850773630208, 'bic': np.float64(-134.19425812437484)}, 2240: {'params': mu          0.070822
omega       0.000026
alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.81427613788163, 'aic': -175.62855227576327, 'bic': np.float64(-160.97430266383603)}, 2260: {'params': mu          0.072945
omega       0.000022
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 100.7323294853328, 'aic': -179.4646589706656, 'bic': np.float64(-164.81040935873835)}, 2280: {'params': mu          0.070647
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alpha[1]    0.448186
alpha[2]    0.039415
alpha[3]    0.039415
beta[1]     0.049269
beta[2]     0.049269
beta[3]     0.049269
beta[4]     0.049269
beta[5]     0.049269
beta[6]     0.049269
Name: params, dtype: float64, 'loglikelihood': 81.23421975247629, 'aic': -140.46843950495258, 'bic': np.float64(-125.81418989302534)}, 2300: {'params': mu          0.047717
omega       0.000058
alpha[1]    0.173361
alpha[2]    0.058414
alpha[3]    0.058414
beta[1]     0.043810
beta[2]     0.043810
beta[3]     0.043810
beta[4]     0.043810
beta[5]     0.043810
beta[6]     0.043810
Name: params, dtype: float64, 'loglikelihood': 86.20935937674861, 'aic': -150.41871875349722, 'bic': np.float64(-135.76446914156998)}, 2320: {'params': mu          0.038281
omega       0.000033
alpha[1]    0.066671
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.29919453349831, 'aic': -174.59838906699662, 'bic': np.float64(-159.94413945506938)}, 2340: {'params': mu          0.035140
omega       0.000022
alpha[1]    0.079121
alpha[2]    0.065777
alpha[3]    0.065777
beta[1]     0.049333
beta[2]     0.049333
beta[3]     0.049333
beta[4]     0.049333
beta[5]     0.049333
beta[6]     0.049333
Name: params, dtype: float64, 'loglikelihood': 103.8781246503168, 'aic': -185.7562493006336, 'bic': np.float64(-171.10199968870637)}, 2360: {'params': mu          7.461554e-02
omega       4.933319e-05
alpha[1]    8.563292e-01
alpha[2]    5.439252e-10
alpha[3]    2.142210e-03
beta[1]     1.413176e-03
beta[2]     1.606659e-03
beta[3]     1.606660e-03
beta[4]     1.606662e-03
beta[5]     1.606664e-03
beta[6]     1.606668e-03
Name: params, dtype: float64, 'loglikelihood': 78.50382987277578, 'aic': -135.00765974555156, 'bic': np.float64(-120.35341013362432)}, 2380: {'params': mu          0.037727
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alpha[1]    0.256851
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alpha[3]    0.043079
beta[1]     0.032310
beta[2]     0.032310
beta[3]     0.032310
beta[4]     0.032310
beta[5]     0.032310
beta[6]     0.032310
Name: params, dtype: float64, 'loglikelihood': 86.01481081598538, 'aic': -150.02962163197077, 'bic': np.float64(-135.37537202004353)}, 2400: {'params': mu          0.040980
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alpha[1]    0.258514
alpha[2]    0.000000
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beta[1]     0.000000
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beta[3]     0.000000
beta[4]     0.000000
beta[5]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 101.04482635857855, 'aic': -180.0896527171571, 'bic': np.float64(-165.43540310522985)}, 2420: {'params': mu          0.074717
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alpha[1]    0.985798
alpha[2]    0.000000
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beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.000000
beta[5]     0.000000
beta[6]     0.014222
Name: params, dtype: float64, 'loglikelihood': 72.8087200389356, 'aic': -123.61744007787121, 'bic': np.float64(-108.96319046594397)}, 2440: {'params': mu          0.038583
omega       0.000061
alpha[1]    0.076040
alpha[2]    0.065997
alpha[3]    0.065997
beta[1]     0.049498
beta[2]     0.049498
beta[3]     0.049498
beta[4]     0.049498
beta[5]     0.049498
beta[6]     0.049498
Name: params, dtype: float64, 'loglikelihood': 87.52992473450527, 'aic': -153.05984946901054, 'bic': np.float64(-138.4055998570833)}, 2460: {'params': mu          0.050942
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 102.02705015868548, 'aic': -182.05410031737097, 'bic': np.float64(-167.39985070544373)}, 2480: {'params': mu          0.046597
omega       0.000021
alpha[1]    0.268859
alpha[2]    0.052613
alpha[3]    0.052089
beta[1]     0.039066
beta[2]     0.039066
beta[3]     0.039066
beta[4]     0.039066
beta[5]     0.039066
beta[6]     0.039066
Name: params, dtype: float64, 'loglikelihood': 98.96904865569039, 'aic': -175.93809731138077, 'bic': np.float64(-161.28384769945353)}, 2500: {'params': mu          0.018332
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alpha[1]    0.066677
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 90.29286794552641, 'aic': -158.58573589105282, 'bic': np.float64(-143.93148627912558)}, 2520: {'params': mu          0.018335
omega       0.000053
alpha[1]    0.066674
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 91.65683927564439, 'aic': -161.31367855128877, 'bic': np.float64(-146.65942893936153)}, 2540: {'params': mu          0.050716
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alpha[1]    0.066699
alpha[2]    0.066664
alpha[3]    0.066664
beta[1]     0.049998
beta[2]     0.049998
beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 84.39961386244887, 'aic': -146.79922772489775, 'bic': np.float64(-132.1449781129705)}, 2560: {'params': mu          0.028276
omega       0.000098
alpha[1]    0.078432
alpha[2]    0.065826
alpha[3]    0.065826
beta[1]     0.049370
beta[2]     0.049370
beta[3]     0.049370
beta[4]     0.049370
beta[5]     0.049370
beta[6]     0.049370
Name: params, dtype: float64, 'loglikelihood': 81.35658968829271, 'aic': -140.71317937658543, 'bic': np.float64(-126.05892976465819)}, 2580: {'params': mu          2.009745e-02
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alpha[1]    9.999990e-01
alpha[2]    3.846797e-11
alpha[3]    8.164410e-11
beta[1]     4.192131e-11
beta[2]     8.508579e-11
beta[3]     6.432855e-11
beta[4]     7.711634e-11
beta[5]     9.606524e-07
beta[6]     4.003534e-08
Name: params, dtype: float64, 'loglikelihood': 110.15864848255958, 'aic': -198.31729696511917, 'bic': np.float64(-183.66304735319193)}, 2600: {'params': mu          0.027062
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alpha[1]    0.461162
alpha[2]    0.038516
alpha[3]    0.038516
beta[1]     0.028895
beta[2]     0.028895
beta[3]     0.028895
beta[4]     0.028895
beta[5]     0.028895
beta[6]     0.028895
Name: params, dtype: float64, 'loglikelihood': 73.72736861168156, 'aic': -125.45473722336311, 'bic': np.float64(-110.80048761143587)}, 2620: {'params': mu          0.068377
omega       0.000016
alpha[1]    0.974759
alpha[2]    0.000000
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beta[1]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 75.68209876105313, 'aic': -129.36419752210625, 'bic': np.float64(-114.70994791017901)}, 2640: {'params': mu          0.012341
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alpha[1]    0.066667
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 104.11819019453992, 'aic': -186.23638038907984, 'bic': np.float64(-171.5821307771526)}, 2660: {'params': mu          0.014381
omega       0.000007
alpha[1]    0.066766
alpha[2]    0.066660
alpha[3]    0.066660
beta[1]     0.049995
beta[2]     0.049995
beta[3]     0.049995
beta[4]     0.049995
beta[5]     0.049995
beta[6]     0.049995
Name: params, dtype: float64, 'loglikelihood': 117.70095285982468, 'aic': -213.40190571964936, 'bic': np.float64(-198.74765610772212)}, 2680: {'params': mu          0.021744
omega       0.000017
alpha[1]    0.160004
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beta[2]     0.045000
beta[3]     0.045000
beta[4]     0.045000
beta[5]     0.045000
beta[6]     0.045000
Name: params, dtype: float64, 'loglikelihood': 103.48708068099364, 'aic': -184.97416136198729, 'bic': np.float64(-170.31991175006004)}, 2700: {'params': mu          0.011413
omega       0.000010
alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 113.34265793067637, 'aic': -204.68531586135273, 'bic': np.float64(-190.0310662494255)}, 2720: {'params': mu          0.008257
omega       0.000005
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 123.88530908532407, 'aic': -225.77061817064813, 'bic': np.float64(-211.1163685587209)}, 2740: {'params': mu          0.012316
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 129.34878039375275, 'aic': -236.6975607875055, 'bic': np.float64(-222.04331117557825)}, 2760: {'params': mu          0.012258
omega       0.000091
alpha[1]    0.456607
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alpha[3]    0.039238
beta[1]     0.048933
beta[2]     0.048933
beta[3]     0.048933
beta[4]     0.048933
beta[5]     0.048933
beta[6]     0.048933
Name: params, dtype: float64, 'loglikelihood': 74.02435661654577, 'aic': -126.04871323309155, 'bic': np.float64(-111.3944636211643)}, 2780: {'params': mu          0.030369
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alpha[1]    0.066663
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alpha[3]    0.066663
beta[1]     0.083329
beta[2]     0.083329
beta[3]     0.083329
beta[4]     0.083329
beta[5]     0.083329
beta[6]     0.083329
Name: params, dtype: float64, 'loglikelihood': 68.98013225505322, 'aic': -115.96026451010644, 'bic': np.float64(-101.3060148981792)}, 2800: {'params': mu          0.035075
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alpha[1]    0.102510
alpha[2]    0.064106
alpha[3]    0.064106
beta[1]     0.048080
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beta[3]     0.048080
beta[4]     0.048080
beta[5]     0.048080
beta[6]     0.048080
Name: params, dtype: float64, 'loglikelihood': 79.14924797984224, 'aic': -136.2984959596845, 'bic': np.float64(-121.64424634775725)}, 2820: {'params': mu          0.054120
omega       0.000064
alpha[1]    0.408656
alpha[2]    0.098513
alpha[3]    0.041646
beta[1]     0.031234
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beta[3]     0.031234
beta[4]     0.031234
beta[5]     0.031234
beta[6]     0.031234
Name: params, dtype: float64, 'loglikelihood': 81.79873481502203, 'aic': -141.59746963004406, 'bic': np.float64(-126.94322001811682)}, 2840: {'params': mu          0.025214
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alpha[1]    0.066675
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 91.98968759337038, 'aic': -161.97937518674075, 'bic': np.float64(-147.3251255748135)}, 2860: {'params': mu          0.014211
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 123.18935696103372, 'aic': -224.37871392206745, 'bic': np.float64(-209.7244643101402)}, 2880: {'params': mu          0.008874
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 111.3385917080893, 'aic': -200.6771834161786, 'bic': np.float64(-186.02293380425135)}, 2900: {'params': mu          0.009212
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 133.84172030706318, 'aic': -245.68344061412637, 'bic': np.float64(-231.02919100219913)}, 2920: {'params': mu          0.015258
omega       0.000005
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 121.69368604506246, 'aic': -221.38737209012493, 'bic': np.float64(-206.73312247819769)}, 2940: {'params': mu          0.020209
omega       0.000002
alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 131.8755029558683, 'aic': -241.75100591173663, 'bic': np.float64(-227.09675629980939)}, 2960: {'params': mu          0.029924
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alpha[1]    0.524653
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alpha[3]    0.033951
beta[1]     0.025463
beta[2]     0.025463
beta[3]     0.025463
beta[4]     0.025463
beta[5]     0.025463
beta[6]     0.025463
Name: params, dtype: float64, 'loglikelihood': 83.12583848546502, 'aic': -144.25167697093005, 'bic': np.float64(-129.5974273590028)}, 2980: {'params': mu          0.034040
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alpha[1]    0.066676
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alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 82.63937469152484, 'aic': -143.27874938304967, 'bic': np.float64(-128.62449977112243)}, 3000: {'params': mu          0.030623
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 130.44135952972795, 'aic': -238.8827190594559, 'bic': np.float64(-224.22846944752865)}, 3020: {'params': mu          0.032181
omega       0.000008
alpha[1]    0.066716
alpha[2]    0.066663
alpha[3]    0.066663
beta[1]     0.116661
beta[2]     0.116661
beta[3]     0.116661
beta[4]     0.116661
beta[5]     0.116661
beta[6]     0.116661
Name: params, dtype: float64, 'loglikelihood': 97.62018388438987, 'aic': -173.24036776877975, 'bic': np.float64(-158.5861181568525)}, 3040: {'params': mu          5.515056e-02
omega       1.290056e-05
alpha[1]    9.999998e-01
alpha[2]    1.561290e-08
alpha[3]    1.830865e-08
beta[1]     1.313948e-08
beta[2]     1.349548e-08
beta[3]     1.366417e-08
beta[4]     1.365541e-08
beta[5]     1.350108e-08
beta[6]     1.320072e-08
Name: params, dtype: float64, 'loglikelihood': 86.92012073120043, 'aic': -151.84024146240085, 'bic': np.float64(-137.1859918504736)}, 3060: {'params': mu          0.018470
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alpha[1]    0.066676
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 89.62873519673487, 'aic': -157.25747039346973, 'bic': np.float64(-142.6032207815425)}, 3080: {'params': mu          1.194601e-02
omega       6.396042e-07
alpha[1]    6.666666e-02
alpha[2]    6.666666e-02
alpha[3]    6.666666e-02
beta[1]     8.333333e-02
beta[2]     8.333333e-02
beta[3]     8.333333e-02
beta[4]     8.333333e-02
beta[5]     8.333333e-02
beta[6]     8.333333e-02
Name: params, dtype: float64, 'loglikelihood': 144.57599266871472, 'aic': -267.15198533742944, 'bic': np.float64(-252.4977357255022)}, 3100: {'params': mu          0.015640
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alpha[1]    0.066669
alpha[2]    0.066666
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beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 104.05394294006904, 'aic': -186.10788588013807, 'bic': np.float64(-171.45363626821083)}, 3120: {'params': mu          0.030116
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alpha[1]    0.066762
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alpha[3]    0.066660
beta[1]     0.049995
beta[2]     0.049995
beta[3]     0.049995
beta[4]     0.049995
beta[5]     0.049995
beta[6]     0.049995
Name: params, dtype: float64, 'loglikelihood': 100.18425935582341, 'aic': -178.36851871164683, 'bic': np.float64(-163.7142690997196)}, 3140: {'params': mu          0.020866
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alpha[1]    0.066668
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 104.45129307540239, 'aic': -186.90258615080478, 'bic': np.float64(-172.24833653887754)}, 3160: {'params': mu          0.025510
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alpha[1]    0.066668
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alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 100.80464249822214, 'aic': -179.60928499644427, 'bic': np.float64(-164.95503538451703)}, 3180: {'params': mu          0.017544
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 125.81252595875222, 'aic': -229.62505191750444, 'bic': np.float64(-214.9708023055772)}, 3200: {'params': mu          0.011951
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 135.53853654508586, 'aic': -249.07707309017172, 'bic': np.float64(-234.42282347824448)}, 3220: {'params': mu          0.015545
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alpha[1]    0.066832
alpha[2]    0.066655
alpha[3]    0.066655
beta[1]     0.049991
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beta[3]     0.049991
beta[4]     0.049991
beta[5]     0.049991
beta[6]     0.049991
Name: params, dtype: float64, 'loglikelihood': 106.05898561253086, 'aic': -190.11797122506172, 'bic': np.float64(-175.46372161313448)}, 3240: {'params': mu          2.432992e-02
omega       8.166732e-07
alpha[1]    6.666666e-02
alpha[2]    6.666666e-02
alpha[3]    6.666666e-02
beta[1]     5.000000e-02
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beta[3]     5.000000e-02
beta[4]     5.000000e-02
beta[5]     5.000000e-02
beta[6]     5.000000e-02
Name: params, dtype: float64, 'loglikelihood': 147.79756895839313, 'aic': -273.59513791678626, 'bic': np.float64(-258.940888304859)}, 3260: {'params': mu          0.025741
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alpha[1]    0.091034
alpha[2]    0.064926
alpha[3]    0.064926
beta[1]     0.081158
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beta[3]     0.081158
beta[4]     0.081158
beta[5]     0.081158
beta[6]     0.081158
Name: params, dtype: float64, 'loglikelihood': 100.63702312111218, 'aic': -179.27404624222436, 'bic': np.float64(-164.61979663029712)}, 3280: {'params': mu          0.032350
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alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 101.72210919958506, 'aic': -181.44421839917013, 'bic': np.float64(-166.78996878724288)}, 3300: {'params': mu          0.037971
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 92.71811678475434, 'aic': -163.4362335695087, 'bic': np.float64(-148.78198395758145)}, 3320: {'params': mu          0.048472
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alpha[1]    0.562586
alpha[2]    0.000151
alpha[3]    0.000151
beta[1]     0.000189
beta[2]     0.000189
beta[3]     0.000189
beta[4]     0.000189
beta[5]     0.000189
beta[6]     0.000189
Name: params, dtype: float64, 'loglikelihood': 81.50260235776106, 'aic': -141.00520471552213, 'bic': np.float64(-126.35095510359488)}, 3340: {'params': mu          0.126949
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alpha[1]    0.999748
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beta[2]     0.000013
beta[3]     0.000013
beta[4]     0.000012
beta[5]     0.000012
beta[6]     0.000012
Name: params, dtype: float64, 'loglikelihood': 61.668697141169254, 'aic': -101.33739428233851, 'bic': np.float64(-86.68314467041127)}, 3360: {'params': mu          0.028956
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alpha[1]    0.066671
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 96.9596356151303, 'aic': -171.9192712302606, 'bic': np.float64(-157.26502161833335)}, 3380: {'params': mu          0.021248
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alpha[1]    0.084405
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beta[1]     0.081750
beta[2]     0.081750
beta[3]     0.081750
beta[4]     0.081750
beta[5]     0.081750
beta[6]     0.081750
Name: params, dtype: float64, 'loglikelihood': 97.08699344273242, 'aic': -172.17398688546484, 'bic': np.float64(-157.5197372735376)}, 3400: {'params': mu          0.054925
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alpha[1]    0.935841
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beta[2]     0.000154
beta[3]     0.000155
beta[4]     0.000189
beta[5]     0.000158
beta[6]     0.000189
Name: params, dtype: float64, 'loglikelihood': 86.45035766197041, 'aic': -150.90071532394083, 'bic': np.float64(-136.2464657120136)}, 3420: {'params': mu          0.026489
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alpha[1]    0.066682
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alpha[3]    0.066666
beta[1]     0.049999
beta[2]     0.049999
beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 109.3730506806474, 'aic': -196.7461013612948, 'bic': np.float64(-182.09185174936755)}, 3440: {'params': mu          0.035588
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alpha[1]    0.066679
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beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
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Name: params, dtype: float64, 'loglikelihood': 107.31341570709527, 'aic': -192.62683141419055, 'bic': np.float64(-177.9725818022633)}, 3460: {'params': mu          0.032289
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alpha[1]    0.498020
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beta[2]     0.018465
beta[3]     0.018465
beta[4]     0.018465
beta[5]     0.018465
beta[6]     0.018465
Name: params, dtype: float64, 'loglikelihood': 87.54879206551936, 'aic': -153.09758413103873, 'bic': np.float64(-138.4433345191115)}, 3480: {'params': mu          0.035842
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alpha[1]    0.999975
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beta[2]     0.000002
beta[3]     0.000002
beta[4]     0.000002
beta[5]     0.000002
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Name: params, dtype: float64, 'loglikelihood': 88.54071904662005, 'aic': -155.0814380932401, 'bic': np.float64(-140.42718848131287)}, 3500: {'params': mu          0.021973
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alpha[1]    0.066809
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beta[2]     0.049992
beta[3]     0.049992
beta[4]     0.049992
beta[5]     0.049992
beta[6]     0.049992
Name: params, dtype: float64, 'loglikelihood': 90.56086838714282, 'aic': -159.12173677428564, 'bic': np.float64(-144.4674871623584)}, 3520: {'params': mu          0.014869
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alpha[1]    0.067994
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alpha[3]    0.066572
beta[1]     0.049929
beta[2]     0.049929
beta[3]     0.049929
beta[4]     0.049929
beta[5]     0.049929
beta[6]     0.049929
Name: params, dtype: float64, 'loglikelihood': 117.46121183797251, 'aic': -212.92242367594503, 'bic': np.float64(-198.26817406401778)}, 3540: {'params': mu          0.022908
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alpha[1]    0.066668
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 115.42069020092585, 'aic': -208.8413804018517, 'bic': np.float64(-194.18713078992445)}, 3560: {'params': mu          0.032178
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alpha[1]    0.066668
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alpha[3]    0.066667
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 118.09974269053343, 'aic': -214.19948538106686, 'bic': np.float64(-199.54523576913962)}, 3580: {'params': mu          0.032987
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alpha[1]    0.997749
alpha[2]    0.001276
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beta[1]     0.001228
beta[2]     0.001228
beta[3]     0.001228
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beta[6]     0.001228
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beta[3]     0.032722
beta[4]     0.032722
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Name: params, dtype: float64, 'loglikelihood': 76.17189719600523, 'aic': -130.34379439201047, 'bic': np.float64(-115.68954478008322)}, 3620: {'params': mu          0.070042
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beta[3]     0.083332
beta[4]     0.083332
beta[5]     0.083332
beta[6]     0.083332
Name: params, dtype: float64, 'loglikelihood': 101.45122873735225, 'aic': -180.9024574747045, 'bic': np.float64(-166.24820786277726)}, 3640: {'params': mu          0.064253
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Name: params, dtype: float64, 'loglikelihood': 51.577162427064486, 'aic': -81.15432485412897, 'bic': np.float64(-66.50007524220173)}, 3660: {'params': mu          4.961968e-01
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alpha[1]    1.000000e+00
alpha[2]    2.235528e-11
alpha[3]    8.502274e-11
beta[1]     2.246418e-11
beta[2]     8.512125e-11
beta[3]     1.690511e-10
beta[4]     2.699949e-10
beta[5]     4.561633e-10
beta[6]     6.797686e-10
Name: params, dtype: float64, 'loglikelihood': 16.021826851767823, 'aic': -10.043653703535647, 'bic': np.float64(4.610595908391595)}, 3680: {'params': mu          5.750689e-02
omega       5.622405e-05
alpha[1]    9.998808e-01
alpha[2]    6.988525e-05
alpha[3]    3.629527e-07
beta[1]     4.929125e-05
beta[2]     4.002844e-07
beta[3]     3.760081e-07
beta[4]     1.393485e-06
beta[5]     2.877971e-06
beta[6]     6.527797e-12
Name: params, dtype: float64, 'loglikelihood': 53.320087741217954, 'aic': -84.64017548243591, 'bic': np.float64(-69.98592587050867)}, 3700: {'params': mu          0.036050
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alpha[1]    0.266043
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beta[3]     0.039144
beta[4]     0.039144
beta[5]     0.039144
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Name: params, dtype: float64, 'loglikelihood': 82.98441955504883, 'aic': -143.96883911009766, 'bic': np.float64(-129.31458949817042)}, 3720: {'params': mu          0.058973
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alpha[1]    0.999972
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beta[3]     0.000002
beta[4]     0.000002
beta[5]     0.000002
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Name: params, dtype: float64, 'loglikelihood': 59.8979553858848, 'aic': -97.7959107717696, 'bic': np.float64(-83.14166115984236)}, 3740: {'params': mu          0.141808
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alpha[1]    0.406722
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alpha[3]    0.042377
beta[1]     0.031783
beta[2]     0.031783
beta[3]     0.031783
beta[4]     0.031783
beta[5]     0.031783
beta[6]     0.031783
Name: params, dtype: float64, 'loglikelihood': 76.89604180949989, 'aic': -131.79208361899978, 'bic': np.float64(-117.13783400707254)}, 3760: {'params': mu          0.111792
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alpha[1]    0.160029
alpha[2]    0.059998
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beta[1]     0.074998
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beta[3]     0.074998
beta[4]     0.074998
beta[5]     0.074998
beta[6]     0.074998
Name: params, dtype: float64, 'loglikelihood': 62.366112693454035, 'aic': -102.73222538690807, 'bic': np.float64(-88.07797577498083)}, 3780: {'params': mu          0.057925
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alpha[1]    0.101729
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beta[5]     0.080203
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Name: params, dtype: float64, 'loglikelihood': 96.66262978371414, 'aic': -171.32525956742828, 'bic': np.float64(-156.67100995550103)}, 3800: {'params': mu          0.041257
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alpha[1]    0.066676
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beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 85.98618998701546, 'aic': -149.97237997403093, 'bic': np.float64(-135.3181303621037)}, 3820: {'params': mu          0.037384
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alpha[1]    0.470659
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beta[1]     0.017511
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beta[3]     0.017511
beta[4]     0.017511
beta[5]     0.017511
beta[6]     0.017511
Name: params, dtype: float64, 'loglikelihood': 85.95278696145135, 'aic': -149.9055739229027, 'bic': np.float64(-135.25132431097546)}, 3840: {'params': mu          0.038826
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alpha[1]    0.168438
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beta[1]     0.044548
beta[2]     0.044548
beta[3]     0.044548
beta[4]     0.044548
beta[5]     0.044548
beta[6]     0.044548
Name: params, dtype: float64, 'loglikelihood': 92.96674083354068, 'aic': -163.93348166708137, 'bic': np.float64(-149.27923205515413)}, 3860: {'params': mu          0.022598
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alpha[1]    0.066668
alpha[2]    0.066667
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beta[1]     0.050000
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beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 114.67726551137078, 'aic': -207.35453102274155, 'bic': np.float64(-192.7002814108143)}, 3880: {'params': mu          0.036770
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alpha[1]    0.555123
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beta[3]     0.022005
beta[4]     0.022005
beta[5]     0.022005
beta[6]     0.022005
Name: params, dtype: float64, 'loglikelihood': 75.79390554025835, 'aic': -129.5878110805167, 'bic': np.float64(-114.93356146858946)}, 3900: {'params': mu          7.234233e-02
omega       1.853933e-05
alpha[1]    9.869757e-01
alpha[2]    3.103902e-07
alpha[3]    3.104024e-07
beta[1]     2.329250e-07
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beta[3]     2.328471e-07
beta[4]     2.328047e-07
beta[5]     2.327713e-07
beta[6]     1.302651e-02
Name: params, dtype: float64, 'loglikelihood': 75.00215916657962, 'aic': -128.00431833315923, 'bic': np.float64(-113.35006872123199)}, 3920: {'params': mu          0.032790
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 108.88882614045843, 'aic': -195.77765228091687, 'bic': np.float64(-181.12340266898963)}, 3940: {'params': mu          0.028085
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alpha[1]    0.066675
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 88.82155033986487, 'aic': -155.64310067972974, 'bic': np.float64(-140.9888510678025)}, 3960: {'params': mu          0.084072
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alpha[1]    0.999964
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beta[2]     0.000002
beta[3]     0.000002
beta[4]     0.000002
beta[5]     0.000002
beta[6]     0.000002
Name: params, dtype: float64, 'loglikelihood': 69.56588355134642, 'aic': -117.13176710269283, 'bic': np.float64(-102.47751749076559)}, 3980: {'params': mu          1.848303e-01
omega       7.689769e-05
alpha[1]    1.000000e+00
alpha[2]    9.967334e-12
alpha[3]    9.730497e-12
beta[1]     1.093764e-11
beta[2]     1.124166e-11
beta[3]     1.157190e-11
beta[4]     1.167375e-11
beta[5]     1.186335e-11
beta[6]     1.199428e-11
Name: params, dtype: float64, 'loglikelihood': 51.782311504251396, 'aic': -81.56462300850279, 'bic': np.float64(-66.91037339657555)}, 4000: {'params': mu          0.062182
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alpha[1]    0.066716
alpha[2]    0.066663
alpha[3]    0.066663
beta[1]     0.049997
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beta[3]     0.049997
beta[4]     0.049997
beta[5]     0.049997
beta[6]     0.049997
Name: params, dtype: float64, 'loglikelihood': 67.55587808181116, 'aic': -113.11175616362232, 'bic': np.float64(-98.45750655169508)}, 4020: {'params': mu          0.038226
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alpha[1]    0.066673
alpha[2]    0.066666
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beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 94.32889787415309, 'aic': -166.65779574830617, 'bic': np.float64(-152.00354613637893)}, 4040: {'params': mu          0.032952
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alpha[1]    0.086827
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beta[2]     0.048920
beta[3]     0.048920
beta[4]     0.048920
beta[5]     0.048920
beta[6]     0.048920
Name: params, dtype: float64, 'loglikelihood': 108.5469439188835, 'aic': -195.093887837767, 'bic': np.float64(-180.43963822583976)}, 4060: {'params': mu          0.024719
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alpha[1]    0.066708
alpha[2]    0.066664
alpha[3]    0.066664
beta[1]     0.049998
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beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 103.72935438398748, 'aic': -185.45870876797497, 'bic': np.float64(-170.80445915604773)}, 4080: {'params': mu          0.009054
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 123.54972871972373, 'aic': -225.09945743944746, 'bic': np.float64(-210.44520782752022)}, 4100: {'params': mu          0.011788
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alpha[1]    0.148084
alpha[2]    0.071917
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beta[2]     0.045000
beta[3]     0.045000
beta[4]     0.045000
beta[5]     0.045000
beta[6]     0.045000
Name: params, dtype: float64, 'loglikelihood': 116.64640425753049, 'aic': -211.29280851506098, 'bic': np.float64(-196.63855890313374)}, 4120: {'params': mu          0.017800
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alpha[1]    0.003334
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beta[1]     0.115000
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beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 129.15591742734517, 'aic': -236.31183485469035, 'bic': np.float64(-221.6575852427631)}, 4140: {'params': mu          0.024967
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alpha[1]    0.066670
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beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 98.9553184642538, 'aic': -175.9106369285076, 'bic': np.float64(-161.25638731658037)}, 4160: {'params': mu          0.019834
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 103.34236572134527, 'aic': -184.68473144269055, 'bic': np.float64(-170.0304818307633)}, 4180: {'params': mu          0.015694
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 126.21685346393555, 'aic': -230.4337069278711, 'bic': np.float64(-215.77945731594386)}, 4200: {'params': mu          0.021698
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alpha[1]    0.999880
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beta[2]     0.000010
beta[3]     0.000010
beta[4]     0.000009
beta[5]     0.000009
beta[6]     0.000009
Name: params, dtype: float64, 'loglikelihood': 69.38116484582153, 'aic': -116.76232969164306, 'bic': np.float64(-102.10808007971582)}, 4220: {'params': mu          1.462988e-01
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beta[1]     2.362437e-08
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beta[3]     2.186638e-08
beta[4]     2.373205e-08
beta[5]     2.839132e-08
beta[6]     3.122440e-08
Name: params, dtype: float64, 'loglikelihood': 44.42472914185559, 'aic': -66.84945828371119, 'bic': np.float64(-52.195208671783945)}, 4240: {'params': mu          0.034498
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alpha[1]    0.066670
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beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 99.56908432198362, 'aic': -177.13816864396725, 'bic': np.float64(-162.48391903204)}, 4260: {'params': mu          0.030856
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alpha[1]    0.066702
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beta[2]     0.049998
beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 98.29775274218899, 'aic': -174.59550548437798, 'bic': np.float64(-159.94125587245074)}, 4280: {'params': mu          0.027368
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beta[3]     0.049890
beta[4]     0.049890
beta[5]     0.049890
beta[6]     0.049890
Name: params, dtype: float64, 'loglikelihood': 103.29007323627924, 'aic': -184.58014647255848, 'bic': np.float64(-169.92589686063124)}, 4300: {'params': mu          0.015123
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alpha[1]    0.066668
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beta[4]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 116.98718761724318, 'aic': -211.97437523448636, 'bic': np.float64(-197.32012562255912)}, 4320: {'params': mu          0.017981
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alpha[1]    0.066667
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Name: params, dtype: float64, 'loglikelihood': 120.60422693797517, 'aic': -219.20845387595034, 'bic': np.float64(-204.5542042640231)}, 4340: {'params': mu          0.020107
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Name: params, dtype: float64, 'loglikelihood': 139.88661263170053, 'aic': -257.77322526340106, 'bic': np.float64(-243.11897565147382)}, 4360: {'params': mu          0.025414
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beta[4]     0.040096
beta[5]     0.040096
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beta[4]     0.045000
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Name: params, dtype: float64, 'loglikelihood': 97.69555093425485, 'aic': -173.3911018685097, 'bic': np.float64(-158.73685225658247)}, 4400: {'params': mu          0.050981
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Name: params, dtype: float64, 'loglikelihood': 90.74406462528952, 'aic': -159.48812925057905, 'bic': np.float64(-144.8338796386518)}, 4420: {'params': mu          0.054444
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beta[3]     0.031363
beta[4]     0.031363
beta[5]     0.031363
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Name: params, dtype: float64, 'loglikelihood': 83.945398837254, 'aic': -145.890797674508, 'bic': np.float64(-131.23654806258077)}, 4440: {'params': mu          0.076585
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beta[5]     0.040208
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Name: params, dtype: float64, 'loglikelihood': 87.12548545791081, 'aic': -152.25097091582163, 'bic': np.float64(-137.59672130389438)}, 4460: {'params': mu          0.051143
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Name: params, dtype: float64, 'loglikelihood': 96.97468369041724, 'aic': -171.94936738083447, 'bic': np.float64(-157.29511776890723)}, 4480: {'params': mu          0.048068
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 99.66298735555574, 'aic': -177.32597471111148, 'bic': np.float64(-165.83622789615384)}, 480: {'params': mu          0.054147
omega       0.000167
alpha[1]    0.213528
alpha[2]    0.056204
alpha[3]    0.056204
beta[1]     0.042160
beta[2]     0.042160
beta[3]     0.042160
beta[4]     0.042160
beta[5]     0.042160
beta[6]     0.042160
Name: params, dtype: float64, 'loglikelihood': 54.25092509828287, 'aic': -86.50185019656574, 'bic': np.float64(-75.01210338160809)}, 500: {'params': mu          0.018471
omega       0.000087
alpha[1]    0.066681
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.049999
beta[2]     0.049999
beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 63.45635880780639, 'aic': -104.91271761561278, 'bic': np.float64(-93.42297080065512)}, 520: {'params': mu          0.016894
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 89.16539275341232, 'aic': -156.33078550682464, 'bic': np.float64(-144.84103869186697)}, 540: {'params': mu          0.038873
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alpha[1]    0.066671
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 69.8355429319238, 'aic': -117.6710858638476, 'bic': np.float64(-106.18133904888994)}, 560: {'params': mu          0.032422
omega       0.000013
alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 82.02561735280179, 'aic': -142.05123470560358, 'bic': np.float64(-130.56148789064594)}, 580: {'params': mu          0.026352
omega       0.000021
alpha[1]    0.066817
alpha[2]    0.066650
alpha[3]    0.066650
beta[1]     0.049987
beta[2]     0.049987
beta[3]     0.049987
beta[4]     0.049987
beta[5]     0.049987
beta[6]     0.049987
Name: params, dtype: float64, 'loglikelihood': 76.75133594976585, 'aic': -131.5026718995317, 'bic': np.float64(-120.01292508457404)}, 600: {'params': mu          0.033751
omega       0.000004
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 94.48798312066705, 'aic': -166.9759662413341, 'bic': np.float64(-155.48621942637646)}, 620: {'params': mu          0.029954
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alpha[1]    0.342926
alpha[2]    0.046934
alpha[3]    0.046934
beta[1]     0.035200
beta[2]     0.035200
beta[3]     0.035200
beta[4]     0.035200
beta[5]     0.035200
beta[6]     0.035200
Name: params, dtype: float64, 'loglikelihood': 61.099465717724385, 'aic': -100.19893143544877, 'bic': np.float64(-88.70918462049111)}, 640: {'params': mu          5.349252e-02
omega       4.060772e-06
alpha[1]    7.724271e-01
alpha[2]    8.610745e-12
alpha[3]    1.482977e-11
beta[1]     1.431376e-11
beta[2]     1.976314e-11
beta[3]     3.335432e-11
beta[4]     1.834124e-11
beta[5]     3.491836e-11
beta[6]     2.275727e-01
Name: params, dtype: float64, 'loglikelihood': 62.45210988166043, 'aic': -102.90421976332085, 'bic': np.float64(-91.4144729483632)}, 660: {'params': mu          0.042462
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 72.36716520677233, 'aic': -122.73433041354465, 'bic': np.float64(-111.244583598587)}, 680: {'params': mu          0.031239
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alpha[1]    0.160017
alpha[2]    0.060104
alpha[3]    0.060104
beta[1]     0.045107
beta[2]     0.045107
beta[3]     0.045107
beta[4]     0.045107
beta[5]     0.045107
beta[6]     0.045107
Name: params, dtype: float64, 'loglikelihood': 67.49445967070186, 'aic': -112.98891934140372, 'bic': np.float64(-101.49917252644606)}, 700: {'params': mu          0.025838
omega       0.000002
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 96.12041385011628, 'aic': -170.24082770023256, 'bic': np.float64(-158.75108088527492)}, 720: {'params': mu          0.023635
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alpha[1]    0.329486
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alpha[3]    0.047894
beta[1]     0.035920
beta[2]     0.035920
beta[3]     0.035920
beta[4]     0.035920
beta[5]     0.035920
beta[6]     0.035920
Name: params, dtype: float64, 'loglikelihood': 73.1025911598516, 'aic': -124.2051823197032, 'bic': np.float64(-112.71543550474554)}, 740: {'params': mu          0.047047
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alpha[1]    0.066672
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 73.853896612179, 'aic': -125.707793224358, 'bic': np.float64(-114.21804640940034)}, 760: {'params': mu          0.033434
omega       0.000002
alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 94.73127190630997, 'aic': -167.46254381261994, 'bic': np.float64(-155.97279699766227)}, 780: {'params': mu          0.034371
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alpha[1]    0.341380
alpha[2]    0.047044
alpha[3]    0.047044
beta[1]     0.035283
beta[2]     0.035283
beta[3]     0.035283
beta[4]     0.035283
beta[5]     0.035283
beta[6]     0.035283
Name: params, dtype: float64, 'loglikelihood': 76.37354587435448, 'aic': -130.74709174870895, 'bic': np.float64(-119.2573449337513)}, 800: {'params': mu          0.026593
omega       0.000002
alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 99.18980711855977, 'aic': -176.37961423711954, 'bic': np.float64(-164.8898674221619)}, 820: {'params': mu          0.037834
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alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 85.96525105133871, 'aic': -149.93050210267742, 'bic': np.float64(-138.44075528771975)}, 840: {'params': mu          0.034974
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alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 80.20252243450564, 'aic': -138.40504486901128, 'bic': np.float64(-126.91529805405362)}, 860: {'params': mu          0.028461
omega       0.000006
alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 89.25391805720628, 'aic': -156.50783611441256, 'bic': np.float64(-145.0180892994549)}, 880: {'params': mu          0.033912
omega       0.000002
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 94.49246889828868, 'aic': -166.98493779657736, 'bic': np.float64(-155.49519098161971)}, 900: {'params': mu          0.043283
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 87.51125679686123, 'aic': -153.02251359372246, 'bic': np.float64(-141.53276677876482)}, 920: {'params': mu          0.035441
omega       0.000019
alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 77.35914105403879, 'aic': -132.71828210807757, 'bic': np.float64(-121.22853529311992)}, 940: {'params': mu          0.033766
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 107.92583479924215, 'aic': -193.8516695984843, 'bic': np.float64(-182.36192278352667)}, 960: {'params': mu          0.032492
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alpha[1]    0.217625
alpha[2]    0.055895
alpha[3]    0.055895
beta[1]     0.041925
beta[2]     0.041925
beta[3]     0.041925
beta[4]     0.041925
beta[5]     0.041925
beta[6]     0.041925
Name: params, dtype: float64, 'loglikelihood': 85.02203576755517, 'aic': -148.04407153511033, 'bic': np.float64(-136.5543247201527)}, 980: {'params': mu          2.835404e-02
omega       2.924251e-05
alpha[1]    9.989862e-01
alpha[2]    3.329353e-10
alpha[3]    4.480378e-10
beta[1]     5.248687e-10
beta[2]     6.239581e-10
beta[3]     9.201551e-10
beta[4]     1.193289e-09
beta[5]     1.439831e-09
beta[6]     1.393526e-09
Name: params, dtype: float64, 'loglikelihood': 65.17855240810816, 'aic': -108.35710481621632, 'bic': np.float64(-96.86735800125867)}, 1000: {'params': mu          0.052890
omega       0.000005
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003334
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 85.44484781304823, 'aic': -148.88969562609645, 'bic': np.float64(-137.3999488111388)}, 1020: {'params': mu          0.067054
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alpha[1]    0.066704
alpha[2]    0.066664
alpha[3]    0.066664
beta[1]     0.049998
beta[2]     0.049998
beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 64.4437570839459, 'aic': -106.8875141678918, 'bic': np.float64(-95.39776735293414)}, 1040: {'params': mu          0.045198
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alpha[1]    0.066668
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 77.00154153455202, 'aic': -132.00308306910404, 'bic': np.float64(-120.51333625414638)}, 1060: {'params': mu          0.029887
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 78.77680506141424, 'aic': -135.55361012282847, 'bic': np.float64(-124.06386330787082)}, 1080: {'params': mu          0.032392
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 85.50538356546242, 'aic': -149.01076713092485, 'bic': np.float64(-137.52102031596718)}, 1100: {'params': mu          0.040095
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alpha[1]    0.160008
alpha[2]    0.059999
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beta[1]     0.045000
beta[2]     0.045000
beta[3]     0.045000
beta[4]     0.045000
beta[5]     0.045000
beta[6]     0.045000
Name: params, dtype: float64, 'loglikelihood': 73.64801146574538, 'aic': -125.29602293149077, 'bic': np.float64(-113.80627611653311)}, 1120: {'params': mu          0.050559
omega       0.000006
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 88.88853365946565, 'aic': -155.7770673189313, 'bic': np.float64(-144.28732050397366)}, 1140: {'params': mu          0.055153
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alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 75.86154079072952, 'aic': -129.72308158145904, 'bic': np.float64(-118.23333476650139)}, 1160: {'params': mu          0.040905
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alpha[1]    0.066683
alpha[2]    0.066665
alpha[3]    0.066665
beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 66.62558571652421, 'aic': -111.25117143304843, 'bic': np.float64(-99.76142461809077)}, 1180: {'params': mu          0.034343
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
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beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 93.90723320111928, 'aic': -165.81446640223857, 'bic': np.float64(-154.32471958728092)}, 1200: {'params': mu          0.039459
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alpha[1]    0.306054
alpha[2]    0.049627
alpha[3]    0.049627
beta[1]     0.037231
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beta[3]     0.037231
beta[4]     0.037231
beta[5]     0.037231
beta[6]     0.037231
Name: params, dtype: float64, 'loglikelihood': 76.74013298314576, 'aic': -131.4802659662915, 'bic': np.float64(-119.99051915133386)}, 1220: {'params': mu          0.030849
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alpha[1]    0.016671
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alpha[3]    0.016667
beta[1]     0.108333
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beta[3]     0.108333
beta[4]     0.108333
beta[5]     0.108333
beta[6]     0.108333
Name: params, dtype: float64, 'loglikelihood': 81.7127237080161, 'aic': -141.4254474160322, 'bic': np.float64(-129.93570060107453)}, 1240: {'params': mu          0.016954
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 82.9842453779781, 'aic': -143.9684907559562, 'bic': np.float64(-132.47874394099853)}, 1260: {'params': mu          0.020266
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 86.83426545080243, 'aic': -151.66853090160487, 'bic': np.float64(-140.17878408664723)}, 1280: {'params': mu          0.036032
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alpha[1]    0.363673
alpha[2]    0.047189
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beta[1]     0.035859
beta[2]     0.035859
beta[3]     0.035859
beta[4]     0.035859
beta[5]     0.035859
beta[6]     0.035859
Name: params, dtype: float64, 'loglikelihood': 67.74223881201107, 'aic': -113.48447762402213, 'bic': np.float64(-101.99473080906448)}, 1300: {'params': mu          0.021354
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 89.76845205267622, 'aic': -157.53690410535245, 'bic': np.float64(-146.0471572903948)}, 1320: {'params': mu          0.031056
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alpha[1]    0.467871
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alpha[3]    0.038009
beta[1]     0.028507
beta[2]     0.028507
beta[3]     0.028507
beta[4]     0.028507
beta[5]     0.028507
beta[6]     0.028507
Name: params, dtype: float64, 'loglikelihood': 71.66786587509849, 'aic': -121.33573175019697, 'bic': np.float64(-109.84598493523931)}, 1340: {'params': mu          0.013148
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.84122347947832, 'aic': -175.68244695895663, 'bic': np.float64(-164.192700143999)}, 1360: {'params': mu          0.019446
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alpha[1]    0.429217
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alpha[3]    0.040770
beta[1]     0.030578
beta[2]     0.030578
beta[3]     0.030578
beta[4]     0.030578
beta[5]     0.030578
beta[6]     0.030578
Name: params, dtype: float64, 'loglikelihood': 85.37687902415462, 'aic': -148.75375804830924, 'bic': np.float64(-137.2640112333516)}, 1380: {'params': mu          0.034509
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 92.81133573639767, 'aic': -163.62267147279533, 'bic': np.float64(-152.1329246578377)}, 1400: {'params': mu          0.042353
omega       0.000013
alpha[1]    0.167228
alpha[2]    0.059484
alpha[3]    0.059484
beta[1]     0.044613
beta[2]     0.044613
beta[3]     0.044613
beta[4]     0.044613
beta[5]     0.044613
beta[6]     0.044613
Name: params, dtype: float64, 'loglikelihood': 81.85989960061083, 'aic': -141.71979920122166, 'bic': np.float64(-130.230052386264)}, 1420: {'params': mu          0.033762
omega       0.000005
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 91.79409988192326, 'aic': -161.58819976384652, 'bic': np.float64(-150.09845294888885)}, 1440: {'params': mu          0.050743
omega       0.000116
alpha[1]    0.000000
alpha[2]    0.000000
alpha[3]    0.000000
beta[1]     0.000000
beta[2]     0.519061
beta[3]     0.000000
beta[4]     0.480959
beta[5]     0.000000
beta[6]     0.000000
Name: params, dtype: float64, 'loglikelihood': 44.77722244589218, 'aic': -67.55444489178436, 'bic': np.float64(-56.0646980768267)}, 1460: {'params': mu          1.751092e-01
omega       1.541706e-03
alpha[1]    7.516513e-01
alpha[2]    1.642522e-14
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     1.620185e-14
beta[4]     7.218500e-14
beta[5]     9.566097e-14
beta[6]     1.169629e-13
Name: params, dtype: float64, 'loglikelihood': 30.146469830571004, 'aic': -38.29293966114201, 'bic': np.float64(-26.803192846184352)}, 1480: {'params': mu          0.028427
omega       0.000005
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 93.22813731066589, 'aic': -164.45627462133177, 'bic': np.float64(-152.96652780637413)}, 1500: {'params': mu          0.023121
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.19558719210129, 'aic': -174.39117438420257, 'bic': np.float64(-162.9014275692449)}, 1520: {'params': mu          0.029715
omega       0.000007
alpha[1]    0.066705
alpha[2]    0.066664
alpha[3]    0.066664
beta[1]     0.049998
beta[2]     0.049998
beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 88.28592227076987, 'aic': -154.57184454153975, 'bic': np.float64(-143.0820977265821)}, 1540: {'params': mu          0.028488
omega       0.000021
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 75.97263582222932, 'aic': -129.94527164445864, 'bic': np.float64(-118.45552482950099)}, 1560: {'params': mu          0.027089
omega       0.000025
alpha[1]    0.066672
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 74.88429487762504, 'aic': -127.76858975525008, 'bic': np.float64(-116.27884294029242)}, 1580: {'params': mu          0.024076
omega       0.000014
alpha[1]    0.066680
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.083332
beta[2]     0.083332
beta[3]     0.083332
beta[4]     0.083332
beta[5]     0.083332
beta[6]     0.083332
Name: params, dtype: float64, 'loglikelihood': 76.65897656454102, 'aic': -131.31795312908204, 'bic': np.float64(-119.82820631412439)}, 1600: {'params': mu          0.045482
omega       0.000048
alpha[1]    0.238041
alpha[2]    0.053441
alpha[3]    0.053439
beta[1]     0.066799
beta[2]     0.066799
beta[3]     0.066799
beta[4]     0.066799
beta[5]     0.066799
beta[6]     0.066799
Name: params, dtype: float64, 'loglikelihood': 63.00642662694819, 'aic': -104.01285325389638, 'bic': np.float64(-92.52310643893873)}, 1620: {'params': mu          3.820340e-02
omega       2.377779e-05
alpha[1]    3.382170e-01
alpha[2]    2.739584e-01
alpha[3]    1.829747e-01
beta[1]     9.376210e-11
beta[2]     1.321651e-10
beta[3]     1.768909e-10
beta[4]     2.202085e-10
beta[5]     2.654080e-10
beta[6]     3.154707e-10
Name: params, dtype: float64, 'loglikelihood': 72.0101484423015, 'aic': -122.020296884603, 'bic': np.float64(-110.53055006964534)}, 1640: {'params': mu          0.021608
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alpha[1]    0.066983
alpha[2]    0.066644
alpha[3]    0.066644
beta[1]     0.049983
beta[2]     0.049983
beta[3]     0.049983
beta[4]     0.049983
beta[5]     0.049983
beta[6]     0.049983
Name: params, dtype: float64, 'loglikelihood': 69.62078531544651, 'aic': -117.24157063089302, 'bic': np.float64(-105.75182381593537)}, 1660: {'params': mu          0.033305
omega       0.000013
alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 81.58107738279585, 'aic': -141.1621547655917, 'bic': np.float64(-129.67240795063407)}, 1680: {'params': mu          0.035937
omega       0.000013
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003334
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 75.60153453907313, 'aic': -129.20306907814626, 'bic': np.float64(-117.7133222631886)}, 1700: {'params': mu          0.064462
omega       0.000014
alpha[1]    0.317392
alpha[2]    0.048758
alpha[3]    0.048758
beta[1]     0.036568
beta[2]     0.036568
beta[3]     0.036568
beta[4]     0.036568
beta[5]     0.036568
beta[6]     0.036568
Name: params, dtype: float64, 'loglikelihood': 78.12390445240209, 'aic': -134.24780890480417, 'bic': np.float64(-122.75806208984652)}, 1720: {'params': mu          7.510600e-02
omega       2.759910e-05
alpha[1]    9.999953e-01
alpha[2]    3.382167e-07
alpha[3]    3.414567e-07
beta[1]     2.576427e-07
beta[2]     2.600991e-07
beta[3]     2.628323e-07
beta[4]     2.645742e-07
beta[5]     2.662121e-07
beta[6]     2.680122e-07
Name: params, dtype: float64, 'loglikelihood': 59.61021865942906, 'aic': -97.22043731885812, 'bic': np.float64(-85.73069050390046)}, 1740: {'params': mu          0.035679
omega       0.000011
alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 83.69539319168219, 'aic': -145.39078638336437, 'bic': np.float64(-133.9010395684067)}, 1760: {'params': mu          0.047320
omega       0.000014
alpha[1]    1.000000
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alpha[3]    0.000000
beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.000000
beta[5]     0.000000
beta[6]     0.000000
Name: params, dtype: float64, 'loglikelihood': 72.13092962027427, 'aic': -122.26185924054855, 'bic': np.float64(-110.77211242559089)}, 1780: {'params': mu          0.020487
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 102.26892983002188, 'aic': -182.53785966004375, 'bic': np.float64(-171.0481128450861)}, 1800: {'params': mu          3.628762e-02
omega       6.184949e-05
alpha[1]    5.619603e-01
alpha[2]    0.000000e+00
alpha[3]    1.486561e-10
beta[1]     0.000000e+00
beta[2]     1.114207e-10
beta[3]     1.115148e-10
beta[4]     1.116319e-10
beta[5]     1.119572e-10
beta[6]     1.122257e-10
Name: params, dtype: float64, 'loglikelihood': 66.6998993547978, 'aic': -111.39979870959559, 'bic': np.float64(-99.91005189463793)}, 1820: {'params': mu          0.011537
omega       0.000002
alpha[1]    0.066709
alpha[2]    0.066664
alpha[3]    0.066664
beta[1]     0.049998
beta[2]     0.049998
beta[3]     0.049998
beta[4]     0.049998
beta[5]     0.049998
beta[6]     0.049998
Name: params, dtype: float64, 'loglikelihood': 99.59054239958208, 'aic': -177.18108479916415, 'bic': np.float64(-165.69133798420648)}, 1840: {'params': mu          0.029069
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 75.2448335018013, 'aic': -128.4896670036026, 'bic': np.float64(-116.99992018864494)}, 1860: {'params': mu          0.019360
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alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 82.51052958501135, 'aic': -143.0210591700227, 'bic': np.float64(-131.53131235506504)}, 1880: {'params': mu          0.031896
omega       0.000039
alpha[1]    0.066674
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 70.59167003624879, 'aic': -119.18334007249757, 'bic': np.float64(-107.69359325753992)}, 1900: {'params': mu          0.044536
omega       0.000013
alpha[1]    0.068920
alpha[2]    0.066506
alpha[3]    0.066506
beta[1]     0.049879
beta[2]     0.049879
beta[3]     0.049879
beta[4]     0.049879
beta[5]     0.049879
beta[6]     0.049879
Name: params, dtype: float64, 'loglikelihood': 81.31069397987163, 'aic': -140.62138795974326, 'bic': np.float64(-129.1316411447856)}, 1920: {'params': mu          0.044698
omega       0.000053
alpha[1]    0.202515
alpha[2]    0.077366
alpha[3]    0.053621
beta[1]     0.040216
beta[2]     0.040216
beta[3]     0.040216
beta[4]     0.040216
beta[5]     0.040216
beta[6]     0.040216
Name: params, dtype: float64, 'loglikelihood': 66.83523735528553, 'aic': -111.67047471057106, 'bic': np.float64(-100.1807278956134)}, 1940: {'params': mu          5.539065e-02
omega       9.235836e-05
alpha[1]    1.000000e+00
alpha[2]    2.488028e-12
alpha[3]    4.956561e-12
beta[1]     8.898881e-12
beta[2]     1.105638e-11
beta[3]     1.368091e-11
beta[4]     1.710206e-11
beta[5]     2.410134e-11
beta[6]     2.736103e-11
Name: params, dtype: float64, 'loglikelihood': 57.46622079030512, 'aic': -92.93244158061025, 'bic': np.float64(-81.44269476565259)}, 1960: {'params': mu          0.010752
omega       0.000009
alpha[1]    0.067237
alpha[2]    0.066626
alpha[3]    0.066626
beta[1]     0.083282
beta[2]     0.083282
beta[3]     0.083282
beta[4]     0.083282
beta[5]     0.083282
beta[6]     0.083282
Name: params, dtype: float64, 'loglikelihood': 80.86880311387725, 'aic': -139.7376062277545, 'bic': np.float64(-128.24785941279686)}, 1980: {'params': mu          0.018454
omega       0.000011
alpha[1]    0.033335
alpha[2]    0.033333
alpha[3]    0.033333
beta[1]     0.066667
beta[2]     0.066667
beta[3]     0.066667
beta[4]     0.066667
beta[5]     0.066667
beta[6]     0.066667
Name: params, dtype: float64, 'loglikelihood': 83.30480517751273, 'aic': -144.60961035502547, 'bic': np.float64(-133.1198635400678)}, 2000: {'params': mu          0.021632
omega       0.000011
alpha[1]    0.167655
alpha[2]    0.057407
alpha[3]    0.057407
beta[1]     0.071759
beta[2]     0.071759
beta[3]     0.071759
beta[4]     0.071759
beta[5]     0.071759
beta[6]     0.071759
Name: params, dtype: float64, 'loglikelihood': 79.79758255555024, 'aic': -137.59516511110047, 'bic': np.float64(-126.10541829614282)}, 2020: {'params': mu          0.025294
omega       0.000016
alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 79.3847054327298, 'aic': -136.7694108654596, 'bic': np.float64(-125.27966405050195)}, 2040: {'params': mu          0.032328
omega       0.000005
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 92.60387623939876, 'aic': -163.20775247879752, 'bic': np.float64(-151.71800566383985)}, 2060: {'params': mu          0.033260
omega       0.000007
alpha[1]    0.066829
alpha[2]    0.066655
alpha[3]    0.066655
beta[1]     0.049991
beta[2]     0.049991
beta[3]     0.049991
beta[4]     0.049991
beta[5]     0.049991
beta[6]     0.049991
Name: params, dtype: float64, 'loglikelihood': 89.2538930249604, 'aic': -156.5077860499208, 'bic': np.float64(-145.01803923496317)}, 2080: {'params': mu          0.035078
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alpha[1]    0.066666
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 75.13012040322326, 'aic': -128.26024080644652, 'bic': np.float64(-116.77049399148886)}, 2100: {'params': mu          0.037232
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alpha[1]    0.490116
alpha[2]    0.000018
alpha[3]    0.000018
beta[1]     0.000014
beta[2]     0.000014
beta[3]     0.000014
beta[4]     0.000014
beta[5]     0.000014
beta[6]     0.000014
Name: params, dtype: float64, 'loglikelihood': 73.01801646861556, 'aic': -124.03603293723111, 'bic': np.float64(-112.54628612227346)}, 2120: {'params': mu          0.029473
omega       0.000001
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.115000
beta[2]     0.115000
beta[3]     0.115000
beta[4]     0.115000
beta[5]     0.115000
beta[6]     0.115000
Name: params, dtype: float64, 'loglikelihood': 100.12432589629856, 'aic': -178.24865179259712, 'bic': np.float64(-166.75890497763947)}, 2140: {'params': mu          0.039865
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alpha[1]    0.089383
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alpha[3]    0.065045
beta[1]     0.048783
beta[2]     0.048783
beta[3]     0.048783
beta[4]     0.048783
beta[5]     0.048783
beta[6]     0.048783
Name: params, dtype: float64, 'loglikelihood': 76.7271579904464, 'aic': -131.4543159808928, 'bic': np.float64(-119.96456916593515)}, 2160: {'params': mu          0.046418
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alpha[1]    0.066668
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alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 89.1235377371525, 'aic': -156.247075474305, 'bic': np.float64(-144.75732865934737)}, 2180: {'params': mu          0.046582
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alpha[1]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 81.0586752002881, 'aic': -140.1173504005762, 'bic': np.float64(-128.62760358561854)}, 2200: {'params': mu          0.050803
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alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.083333
beta[2]     0.083333
beta[3]     0.083333
beta[4]     0.083333
beta[5]     0.083333
beta[6]     0.083333
Name: params, dtype: float64, 'loglikelihood': 79.79611022602461, 'aic': -137.59222045204922, 'bic': np.float64(-126.10247363709156)}, 2220: {'params': mu          8.482488e-02
omega       2.014708e-05
alpha[1]    1.000000e+00
alpha[2]    1.779956e-11
alpha[3]    5.432070e-11
beta[1]     2.193566e-11
beta[2]     5.846361e-11
beta[3]     9.433163e-11
beta[4]     7.033998e-11
beta[5]     6.370607e-11
beta[6]     7.936356e-11
Name: params, dtype: float64, 'loglikelihood': 69.05596637523044, 'aic': -116.11193275046088, 'bic': np.float64(-104.62218593550323)}, 2240: {'params': mu          0.070566
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alpha[1]    0.067659
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alpha[3]    0.066596
beta[1]     0.049947
beta[2]     0.049947
beta[3]     0.049947
beta[4]     0.049947
beta[5]     0.049947
beta[6]     0.049947
Name: params, dtype: float64, 'loglikelihood': 73.47729671255361, 'aic': -124.95459342510722, 'bic': np.float64(-113.46484661014956)}, 2260: {'params': mu          0.074178
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alpha[1]    0.066669
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 77.57801646423675, 'aic': -133.1560329284735, 'bic': np.float64(-121.66628611351585)}, 2280: {'params': mu          0.071156
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alpha[1]    0.303121
alpha[2]    0.044259
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beta[3]     0.040540
beta[4]     0.040540
beta[5]     0.040540
beta[6]     0.040540
Name: params, dtype: float64, 'loglikelihood': 72.74191625672162, 'aic': -123.48383251344325, 'bic': np.float64(-111.99408569848559)}, 2300: {'params': mu          0.037175
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alpha[1]    0.514683
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alpha[3]    0.034511
beta[1]     0.025883
beta[2]     0.025883
beta[3]     0.025883
beta[4]     0.025883
beta[5]     0.025883
beta[6]     0.025883
Name: params, dtype: float64, 'loglikelihood': 63.37562803086827, 'aic': -104.75125606173654, 'bic': np.float64(-93.26150924677889)}, 2320: {'params': mu          0.039306
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alpha[1]    0.066681
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beta[1]     0.049999
beta[2]     0.049999
beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 70.96715992267201, 'aic': -119.93431984534402, 'bic': np.float64(-108.44457303038637)}, 2340: {'params': mu          0.033466
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alpha[1]    0.003334
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 82.84965670038787, 'aic': -143.69931340077574, 'bic': np.float64(-132.2095665858181)}, 2360: {'params': mu          7.635810e-02
omega       2.494538e-05
alpha[1]    8.088398e-01
alpha[2]    4.824444e-07
alpha[3]    4.858608e-07
beta[1]     3.681826e-07
beta[2]     3.687249e-07
beta[3]     3.692061e-07
beta[4]     3.698265e-07
beta[5]     3.704117e-07
beta[6]     3.709974e-07
Name: params, dtype: float64, 'loglikelihood': 63.899868947953976, 'aic': -105.79973789590795, 'bic': np.float64(-94.3099910809503)}, 2380: {'params': mu          0.040568
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alpha[1]    0.066681
alpha[2]    0.066666
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beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 58.38426578142457, 'aic': -94.76853156284913, 'bic': np.float64(-83.27878474789148)}, 2400: {'params': mu          0.040375
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 86.0965495058881, 'aic': -150.1930990117762, 'bic': np.float64(-138.70335219681857)}, 2420: {'params': mu          0.078738
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alpha[1]    0.948985
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beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 59.26185190805122, 'aic': -96.52370381610244, 'bic': np.float64(-85.03395700114478)}, 2440: {'params': mu          0.034876
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alpha[1]    0.066770
alpha[2]    0.066659
alpha[3]    0.066659
beta[1]     0.049994
beta[2]     0.049994
beta[3]     0.049994
beta[4]     0.049994
beta[5]     0.049994
beta[6]     0.049994
Name: params, dtype: float64, 'loglikelihood': 66.97810179697912, 'aic': -111.95620359395824, 'bic': np.float64(-100.46645677900058)}, 2460: {'params': mu          0.050305
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alpha[1]    0.003336
alpha[2]    0.003333
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beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 73.29665132983894, 'aic': -124.59330265967787, 'bic': np.float64(-113.10355584472022)}, 2480: {'params': mu          0.048513
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alpha[1]    0.068590
alpha[2]    0.066529
alpha[3]    0.066529
beta[1]     0.049897
beta[2]     0.049897
beta[3]     0.049897
beta[4]     0.049897
beta[5]     0.049897
beta[6]     0.049897
Name: params, dtype: float64, 'loglikelihood': 78.65338619926268, 'aic': -135.30677239852537, 'bic': np.float64(-123.81702558356771)}, 2500: {'params': mu          0.018380
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alpha[1]    0.897406
alpha[2]    0.102422
alpha[3]    0.000002
beta[1]     0.000001
beta[2]     0.000001
beta[3]     0.000001
beta[4]     0.000001
beta[5]     0.000001
beta[6]     0.000001
Name: params, dtype: float64, 'loglikelihood': 68.0463341566203, 'aic': -114.09266831324061, 'bic': np.float64(-102.60292149828295)}, 2520: {'params': mu          0.015180
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alpha[1]    0.091251
alpha[2]    0.064911
alpha[3]    0.064911
beta[1]     0.048683
beta[2]     0.048683
beta[3]     0.048683
beta[4]     0.048683
beta[5]     0.048683
beta[6]     0.048683
Name: params, dtype: float64, 'loglikelihood': 85.33632722110428, 'aic': -148.67265444220857, 'bic': np.float64(-137.18290762725093)}, 2540: {'params': mu          0.052265
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alpha[1]    0.121613
alpha[2]    0.062742
alpha[3]    0.062742
beta[1]     0.047056
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beta[3]     0.047056
beta[4]     0.047056
beta[5]     0.047056
beta[6]     0.047056
Name: params, dtype: float64, 'loglikelihood': 61.39072904088012, 'aic': -100.78145808176023, 'bic': np.float64(-89.29171126680258)}, 2560: {'params': mu          0.036803
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alpha[1]    0.797370
alpha[2]    0.000007
alpha[3]    0.000007
beta[1]     0.000005
beta[2]     0.000005
beta[3]     0.000005
beta[4]     0.000005
beta[5]     0.000005
beta[6]     0.000005
Name: params, dtype: float64, 'loglikelihood': 62.729020621586066, 'aic': -103.45804124317213, 'bic': np.float64(-91.96829442821448)}, 2580: {'params': mu          0.024555
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alpha[1]    0.066669
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 84.08621588713201, 'aic': -146.17243177426403, 'bic': np.float64(-134.68268495930636)}, 2600: {'params': mu          1.850861e-02
omega       1.327691e-05
alpha[1]    9.653792e-01
alpha[2]    3.040824e-12
alpha[3]    1.024014e-11
beta[1]     2.691925e-12
beta[2]     2.269155e-11
beta[3]     5.652070e-11
beta[4]     9.160487e-11
beta[5]     1.269820e-10
beta[6]     1.889533e-10
Name: params, dtype: float64, 'loglikelihood': 68.54657865605456, 'aic': -115.09315731210913, 'bic': np.float64(-103.60341049715147)}, 2620: {'params': mu          0.063209
omega       0.000111
alpha[1]    0.332794
alpha[2]    0.047658
alpha[3]    0.047658
beta[1]     0.035743
beta[2]     0.035743
beta[3]     0.035743
beta[4]     0.035743
beta[5]     0.035743
beta[6]     0.035743
Name: params, dtype: float64, 'loglikelihood': 59.064724323993445, 'aic': -96.12944864798689, 'bic': np.float64(-84.63970183302924)}, 2640: {'params': mu          0.014062
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alpha[1]    0.066671
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alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 74.44992597483376, 'aic': -126.89985194966752, 'bic': np.float64(-115.41010513470987)}, 2660: {'params': mu          0.013386
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 98.00706031461452, 'aic': -174.01412062922904, 'bic': np.float64(-162.52437381427137)}, 2680: {'params': mu          0.024350
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alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 79.59000232406584, 'aic': -137.18000464813167, 'bic': np.float64(-125.69025783317402)}, 2700: {'params': mu          0.012855
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alpha[1]    0.066670
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 91.71528942129665, 'aic': -161.4305788425933, 'bic': np.float64(-149.94083202763562)}, 2720: {'params': mu          0.007417
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 100.78887329354262, 'aic': -179.57774658708524, 'bic': np.float64(-168.0879997721276)}, 2740: {'params': mu          0.013059
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alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 99.30076723440055, 'aic': -176.6015344688011, 'bic': np.float64(-165.11178765384346)}, 2760: {'params': mu          0.011979
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alpha[1]    0.382105
alpha[2]    0.044135
alpha[3]    0.044135
beta[1]     0.033102
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beta[3]     0.033102
beta[4]     0.033102
beta[5]     0.033102
beta[6]     0.033102
Name: params, dtype: float64, 'loglikelihood': 64.31758498194206, 'aic': -106.63516996388412, 'bic': np.float64(-95.14542314892647)}, 2780: {'params': mu          0.059587
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alpha[1]    0.993937
alpha[2]    0.000398
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beta[2]     0.000039
beta[3]     0.000039
beta[4]     0.000039
beta[5]     0.000039
beta[6]     0.000039
Name: params, dtype: float64, 'loglikelihood': 59.3474808083181, 'aic': -96.6949616166362, 'bic': np.float64(-85.20521480167855)}, 2800: {'params': mu          2.921086e-02
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alpha[1]    9.999938e-01
alpha[2]    2.114707e-06
alpha[3]    3.147770e-07
beta[1]     2.370751e-07
beta[2]     2.374313e-07
beta[3]     2.377636e-07
beta[4]     2.381257e-07
beta[5]     2.383725e-07
beta[6]     2.385025e-07
Name: params, dtype: float64, 'loglikelihood': 71.8682984619416, 'aic': -121.73659692388321, 'bic': np.float64(-110.24685010892556)}, 2820: {'params': mu          0.057973
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alpha[1]    0.999005
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alpha[3]    0.000149
beta[1]     0.000186
beta[2]     0.000186
beta[3]     0.000186
beta[4]     0.000186
beta[5]     0.000186
beta[6]     0.000186
Name: params, dtype: float64, 'loglikelihood': 73.43490160273386, 'aic': -124.86980320546772, 'bic': np.float64(-113.38005639051006)}, 2840: {'params': mu          0.028307
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alpha[1]    0.164347
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beta[1]     0.044767
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beta[3]     0.044767
beta[4]     0.044767
beta[5]     0.044767
beta[6]     0.044767
Name: params, dtype: float64, 'loglikelihood': 77.08418554716047, 'aic': -132.16837109432095, 'bic': np.float64(-120.67862427936329)}, 2860: {'params': mu          0.012529
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alpha[1]    0.067675
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alpha[3]    0.066595
beta[1]     0.049946
beta[2]     0.049946
beta[3]     0.049946
beta[4]     0.049946
beta[5]     0.049946
beta[6]     0.049946
Name: params, dtype: float64, 'loglikelihood': 93.25725659589098, 'aic': -164.51451319178196, 'bic': np.float64(-153.0247663768243)}, 2880: {'params': mu          0.010906
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alpha[1]    0.066677
alpha[2]    0.066666
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beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 82.48042203969717, 'aic': -142.96084407939435, 'bic': np.float64(-131.4710972644367)}, 2900: {'params': mu          0.008422
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 100.91501683881279, 'aic': -179.83003367762558, 'bic': np.float64(-168.34028686266794)}, 2920: {'params': mu          0.014101
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alpha[1]    0.066668
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 94.9007823268474, 'aic': -167.8015646536948, 'bic': np.float64(-156.31181783873717)}, 2940: {'params': mu          0.019567
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 99.56049690668185, 'aic': -177.1209938133637, 'bic': np.float64(-165.63124699840603)}, 2960: {'params': mu          0.025798
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alpha[1]    0.385845
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alpha[3]    0.043868
beta[1]     0.032901
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beta[3]     0.032901
beta[4]     0.032901
beta[5]     0.032901
beta[6]     0.032901
Name: params, dtype: float64, 'loglikelihood': 68.98711938775988, 'aic': -115.97423877551975, 'bic': np.float64(-104.4844919605621)}, 2980: {'params': mu          4.388919e-02
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alpha[1]    5.471407e-01
alpha[2]    2.002501e-16
alpha[3]    0.000000e+00
beta[1]     3.094001e-17
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     9.126321e-16
beta[5]     3.365405e-16
beta[6]     5.977496e-16
Name: params, dtype: float64, 'loglikelihood': 60.5501592163052, 'aic': -99.1003184326104, 'bic': np.float64(-87.61057161765274)}, 3000: {'params': mu          0.030343
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 99.25978399550968, 'aic': -176.51956799101936, 'bic': np.float64(-165.02982117606172)}, 3020: {'params': mu          0.030354
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 99.7960099408557, 'aic': -177.5920198817114, 'bic': np.float64(-166.10227306675375)}, 3040: {'params': mu          0.055632
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alpha[1]    0.066686
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alpha[3]    0.066665
beta[1]     0.049999
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beta[3]     0.049999
beta[4]     0.049999
beta[5]     0.049999
beta[6]     0.049999
Name: params, dtype: float64, 'loglikelihood': 62.50197394450541, 'aic': -103.00394788901082, 'bic': np.float64(-91.51420107405316)}, 3060: {'params': mu          0.022180
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alpha[1]    0.068680
alpha[2]    0.066523
alpha[3]    0.066523
beta[1]     0.049892
beta[2]     0.049892
beta[3]     0.049892
beta[4]     0.049892
beta[5]     0.049892
beta[6]     0.049892
Name: params, dtype: float64, 'loglikelihood': 67.14764029296236, 'aic': -112.29528058592473, 'bic': np.float64(-100.80553377096707)}, 3080: {'params': mu          0.011724
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alpha[1]    0.066667
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alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 107.47444982350318, 'aic': -192.94889964700636, 'bic': np.float64(-181.4591528320487)}, 3100: {'params': mu          0.014245
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alpha[1]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 104.15035718610764, 'aic': -186.30071437221528, 'bic': np.float64(-174.81096755725764)}, 3120: {'params': mu          0.033036
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alpha[1]    0.066670
alpha[2]    0.066666
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beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 77.3295527485645, 'aic': -132.659105497129, 'bic': np.float64(-121.16935868217134)}, 3140: {'params': mu          0.019658
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alpha[1]    0.003333
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 81.2754456674214, 'aic': -140.5508913348428, 'bic': np.float64(-129.06114451988515)}, 3160: {'params': mu          0.028663
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alpha[1]    0.066670
alpha[2]    0.066666
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beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 77.67427682395584, 'aic': -133.34855364791167, 'bic': np.float64(-121.85880683295402)}, 3180: {'params': mu          0.018197
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
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beta[4]     1.228351e-08
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Name: params, dtype: float64, 'loglikelihood': 76.91175095910664, 'aic': -131.82350191821328, 'bic': np.float64(-120.33375510325563)}, 3300: {'params': mu          0.032490
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Name: params, dtype: float64, 'loglikelihood': 70.71815840152507, 'aic': -119.43631680305015, 'bic': np.float64(-107.94656998809249)}, 3320: {'params': mu          0.047481
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Name: params, dtype: float64, 'loglikelihood': 78.88603106807922, 'aic': -135.77206213615844, 'bic': np.float64(-124.28231532120078)}, 3340: {'params': mu          0.127338
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Name: params, dtype: float64, 'loglikelihood': 75.63024399216917, 'aic': -129.26048798433834, 'bic': np.float64(-117.77074116938068)}, 3380: {'params': mu          0.019938
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Name: params, dtype: float64, 'loglikelihood': 88.9366643543063, 'aic': -155.8733287086126, 'bic': np.float64(-144.38358189365493)}, 3400: {'params': mu          0.048855
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Name: params, dtype: float64, 'loglikelihood': 64.8516448248384, 'aic': -107.7032896496768, 'bic': np.float64(-96.21354283471915)}, 3420: {'params': mu          0.026117
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Name: params, dtype: float64, 'loglikelihood': 84.6822120022657, 'aic': -147.3644240045314, 'bic': np.float64(-135.87467718957373)}, 3440: {'params': mu          0.033832
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Name: params, dtype: float64, 'loglikelihood': 80.61205690670954, 'aic': -139.22411381341908, 'bic': np.float64(-127.73436699846143)}, 3460: {'params': mu          0.035329
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Name: params, dtype: float64, 'loglikelihood': 67.57905229386255, 'aic': -113.15810458772509, 'bic': np.float64(-101.66835777276744)}, 3480: {'params': mu          0.021882
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Name: params, dtype: float64, 'loglikelihood': 68.33755767936736, 'aic': -114.67511535873473, 'bic': np.float64(-103.18536854377707)}, 3500: {'params': mu          0.025795
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Name: params, dtype: float64, 'loglikelihood': 66.82190427110571, 'aic': -111.64380854221142, 'bic': np.float64(-100.15406172725376)}, 3520: {'params': mu          0.013352
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Name: params, dtype: float64, 'loglikelihood': 94.47467111709915, 'aic': -166.9493422341983, 'bic': np.float64(-155.45959541924066)}, 3540: {'params': mu          0.021693
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Name: params, dtype: float64, 'loglikelihood': 90.6889961997666, 'aic': -159.3779923995332, 'bic': np.float64(-147.88824558457554)}, 3560: {'params': mu          0.030892
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Name: params, dtype: float64, 'loglikelihood': 91.42372849004398, 'aic': -160.84745698008797, 'bic': np.float64(-149.3577101651303)}, 3580: {'params': mu          0.031909
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Name: params, dtype: float64, 'loglikelihood': 78.38141169736572, 'aic': -134.76282339473144, 'bic': np.float64(-123.27307657977379)}, 3600: {'params': mu          0.026198
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Name: params, dtype: float64, 'loglikelihood': 71.43274273747909, 'aic': -120.86548547495818, 'bic': np.float64(-109.37573866000052)}, 3620: {'params': mu          0.071209
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Name: params, dtype: float64, 'loglikelihood': 73.2175600549251, 'aic': -124.4351201098502, 'bic': np.float64(-112.94537329489255)}, 3640: {'params': mu          0.058086
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Name: params, dtype: float64, 'loglikelihood': 50.47192224923429, 'aic': -78.94384449846858, 'bic': np.float64(-67.45409768351092)}, 3660: {'params': mu          4.977916e-01
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beta[4]     3.694609e-16
beta[5]     6.206307e-16
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Name: params, dtype: float64, 'loglikelihood': 15.54252227483506, 'aic': -9.085044549670119, 'bic': np.float64(2.4047022652875363)}, 3680: {'params': mu          6.971908e-02
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Name: params, dtype: float64, 'loglikelihood': 38.936371409237545, 'aic': -55.87274281847509, 'bic': np.float64(-44.382996003517434)}, 3700: {'params': mu          0.032849
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Name: params, dtype: float64, 'loglikelihood': 69.41693705060115, 'aic': -116.8338741012023, 'bic': np.float64(-105.34412728624464)}, 3720: {'params': mu          0.058217
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Name: params, dtype: float64, 'loglikelihood': 52.92596366765632, 'aic': -83.85192733531264, 'bic': np.float64(-72.36218052035498)}, 3740: {'params': mu          0.141327
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Name: params, dtype: float64, 'loglikelihood': 76.8426335876915, 'aic': -131.685267175383, 'bic': np.float64(-120.19552036042533)}, 3760: {'params': mu          0.120145
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Name: params, dtype: float64, 'loglikelihood': 56.16165326381087, 'aic': -90.32330652762174, 'bic': np.float64(-78.83355971266408)}, 3780: {'params': mu          0.059112
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Name: params, dtype: float64, 'loglikelihood': 90.90973056332788, 'aic': -159.81946112665577, 'bic': np.float64(-148.32971431169813)}, 3800: {'params': mu          0.041375
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Name: params, dtype: float64, 'loglikelihood': 59.80943053664417, 'aic': -97.61886107328834, 'bic': np.float64(-86.12911425833069)}, 3820: {'params': mu          0.028968
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Name: params, dtype: float64, 'loglikelihood': 63.80789026730083, 'aic': -105.61578053460165, 'bic': np.float64(-94.126033719644)}, 3840: {'params': mu          0.045196
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Name: params, dtype: float64, 'loglikelihood': 80.60380045996737, 'aic': -139.20760091993475, 'bic': np.float64(-127.71785410497709)}, 3860: {'params': mu          0.021234
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Name: params, dtype: float64, 'loglikelihood': 84.96902751510005, 'aic': -147.9380550302001, 'bic': np.float64(-136.44830821524243)}, 3880: {'params': mu          3.218376e-02
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Name: params, dtype: float64, 'loglikelihood': 70.00484485230568, 'aic': -118.00968970461136, 'bic': np.float64(-106.5199428896537)}, 3900: {'params': mu          0.072443
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Name: params, dtype: float64, 'loglikelihood': 62.806746462217646, 'aic': -103.61349292443529, 'bic': np.float64(-92.12374610947764)}, 3920: {'params': mu          0.035417
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Name: params, dtype: float64, 'loglikelihood': 86.21505703921727, 'aic': -150.43011407843454, 'bic': np.float64(-138.9403672634769)}, 3940: {'params': mu          0.026170
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Name: params, dtype: float64, 'loglikelihood': 89.91594898499157, 'aic': -157.83189796998315, 'bic': np.float64(-146.34215115502548)}, 3960: {'params': mu          0.079783
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Name: params, dtype: float64, 'loglikelihood': 53.04856198006983, 'aic': -84.09712396013965, 'bic': np.float64(-72.607377145182)}, 3980: {'params': mu          0.180270
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Name: params, dtype: float64, 'loglikelihood': 50.340678700185535, 'aic': -78.68135740037107, 'bic': np.float64(-67.19161058541341)}, 4000: {'params': mu          0.064153
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Name: params, dtype: float64, 'loglikelihood': 54.51238423917377, 'aic': -87.02476847834754, 'bic': np.float64(-75.53502166338988)}, 4020: {'params': mu          0.033251
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Name: params, dtype: float64, 'loglikelihood': 71.17710785319899, 'aic': -120.35421570639798, 'bic': np.float64(-108.86446889144032)}, 4040: {'params': mu          0.035037
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Name: params, dtype: float64, 'loglikelihood': 82.62078335737162, 'aic': -143.24156671474324, 'bic': np.float64(-131.75181989978557)}, 4060: {'params': mu          0.026507
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Name: params, dtype: float64, 'loglikelihood': 94.51276587404467, 'aic': -167.02553174808935, 'bic': np.float64(-155.5357849331317)}, 4080: {'params': mu          0.009384
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alpha[1]    0.066668
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beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 44.0861725304937, 'aic': -66.1723450609874, 'bic': np.float64(-66.76733342137895)}, 60: {'params': mu          0.030734
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 33.29774088624624, 'aic': -44.59548177249248, 'bic': np.float64(-45.19047013288403)}, 80: {'params': mu          0.020392
omega       0.000002
alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.30316544306467, 'aic': -44.60633088612934, 'bic': np.float64(-45.201319246520896)}, 100: {'params': mu          0.025702
omega       0.000007
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.350235379157915, 'aic': -36.70047075831583, 'bic': np.float64(-37.295459118707385)}, 120: {'params': mu          0.028732
omega       0.000002
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.53158113966819, 'aic': -45.06316227933638, 'bic': np.float64(-45.658150639727936)}, 140: {'params': mu          2.605901e-02
omega       9.895119e-08
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 44.08403352700185, 'aic': -66.1680670540037, 'bic': np.float64(-66.76305541439525)}, 160: {'params': mu          0.014966
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.15649533567223, 'aic': -48.312990671344465, 'bic': np.float64(-48.90797903173602)}, 180: {'params': mu          0.013182
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.622464022138274, 'aic': -49.24492804427655, 'bic': np.float64(-49.8399164046681)}, 200: {'params': mu          2.284738e-02
omega       4.635927e-08
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 46.74066680876264, 'aic': -71.48133361752528, 'bic': np.float64(-72.07632197791683)}, 220: {'params': mu          0.010660
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alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 27.662900602188888, 'aic': -33.325801204377775, 'bic': np.float64(-33.92078956476933)}, 240: {'params': mu          0.014854
omega       0.000003
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.936672583056087, 'aic': -41.87334516611217, 'bic': np.float64(-42.46833352650373)}, 260: {'params': mu          0.016115
omega       0.000009
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.427603511959557, 'aic': -34.855207023919114, 'bic': np.float64(-35.45019538431067)}, 280: {'params': mu          2.629171e-02
omega       5.436481e-07
alpha[1]    3.333388e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 38.12708659756589, 'aic': -54.254173195131784, 'bic': np.float64(-54.84916155552334)}, 300: {'params': mu          0.014952
omega       0.000003
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.74304859706678, 'aic': -43.48609719413356, 'bic': np.float64(-44.08108555452512)}, 320: {'params': mu          2.123788e-02
omega       4.484298e-07
alpha[1]    3.333333e-03
alpha[2]    3.333366e-03
alpha[3]    3.333390e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 38.80780379668105, 'aic': -55.6156075933621, 'bic': np.float64(-56.21059595375365)}, 340: {'params': mu          0.017399
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.58395049104528, 'aic': -39.16790098209056, 'bic': np.float64(-39.76288934248211)}, 360: {'params': mu          0.036359
omega       0.000004
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.78943602311473, 'aic': -39.57887204622946, 'bic': np.float64(-40.17386040662102)}, 380: {'params': mu          0.020136
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 32.43107822849355, 'aic': -42.862156456987094, 'bic': np.float64(-43.45714481737865)}, 400: {'params': mu          0.027231
omega       0.000019
alpha[1]    0.003338
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081669
beta[2]     0.081669
beta[3]     0.081670
beta[4]     0.081670
beta[5]     0.081670
beta[6]     0.081669
Name: params, dtype: float64, 'loglikelihood': 25.638536800166243, 'aic': -29.277073600332486, 'bic': np.float64(-29.87206196072404)}, 420: {'params': mu          0.025384
omega       0.000003
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.221185515496984, 'aic': -42.44237103099397, 'bic': np.float64(-43.03735939138552)}, 440: {'params': mu          6.332235e-03
omega       9.631604e-08
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 44.182097731921075, 'aic': -66.36419546384215, 'bic': np.float64(-66.9591838242337)}, 460: {'params': mu          0.017967
omega       0.000003
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.36061899286954, 'aic': -42.72123798573908, 'bic': np.float64(-43.316226346130634)}, 480: {'params': mu          1.915684e-02
omega       9.687900e-07
alpha[1]    3.333332e-03
alpha[2]    3.333332e-03
alpha[3]    3.333332e-03
beta[1]     8.166669e-02
beta[2]     8.166669e-02
beta[3]     8.166669e-02
beta[4]     8.166669e-02
beta[5]     8.166669e-02
beta[6]     8.166669e-02
Name: params, dtype: float64, 'loglikelihood': 36.10304837679128, 'aic': -50.20609675358256, 'bic': np.float64(-50.80108511397411)}, 500: {'params': mu          2.324008e-02
omega       1.940076e-06
alpha[1]    7.331282e-01
alpha[2]    1.346067e-08
alpha[3]    1.349347e-08
beta[1]     3.297467e-07
beta[2]     3.297661e-07
beta[3]     1.806783e-02
beta[4]     1.989127e-02
beta[5]     3.297833e-07
beta[6]     3.297580e-07
Name: params, dtype: float64, 'loglikelihood': 20.65875645190614, 'aic': -19.31751290381228, 'bic': np.float64(-19.912501264203833)}, 520: {'params': mu          0.012779
omega       0.000004
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.454621403953276, 'aic': -40.90924280790655, 'bic': np.float64(-41.504231168298105)}, 540: {'params': mu          0.026848
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alpha[1]    0.003343
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 25.718167702085964, 'aic': -29.436335404171928, 'bic': np.float64(-30.03132376456348)}, 560: {'params': mu          0.029794
omega       0.000009
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.33653233176768, 'aic': -34.67306466353536, 'bic': np.float64(-35.26805302392691)}, 580: {'params': mu          0.028634
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alpha[1]    0.066668
alpha[2]    0.066668
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050001
beta[5]     0.050001
beta[6]     0.050001
Name: params, dtype: float64, 'loglikelihood': 23.943615939846662, 'aic': -25.887231879693324, 'bic': np.float64(-26.482220240084878)}, 600: {'params': mu          0.035413
omega       0.000005
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 30.666414195238826, 'aic': -39.33282839047765, 'bic': np.float64(-39.927816750869205)}, 620: {'params': mu          0.026130
omega       0.000003
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.94183865151633, 'aic': -41.88367730303266, 'bic': np.float64(-42.478665663424216)}, 640: {'params': mu          0.062764
omega       0.000004
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.007077599347674, 'aic': -40.01415519869535, 'bic': np.float64(-40.6091435590869)}, 660: {'params': mu          3.513559e-02
omega       8.960153e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 36.37977577457081, 'aic': -50.75955154914162, 'bic': np.float64(-51.35453990953317)}, 680: {'params': mu          0.046654
omega       0.000008
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.8673529110486, 'aic': -35.7347058220972, 'bic': np.float64(-36.32969418248875)}, 700: {'params': mu          0.026742
omega       0.000001
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.4909898405345, 'aic': -48.98197968106901, 'bic': np.float64(-49.57696804146056)}, 720: {'params': mu          2.033222e-02
omega       6.417198e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333478e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 37.55350687163264, 'aic': -53.107013743265284, 'bic': np.float64(-53.70200210365684)}, 740: {'params': mu          0.050171
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alpha[1]    0.066667
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 26.390874089697686, 'aic': -30.781748179395372, 'bic': np.float64(-31.376736539786926)}, 760: {'params': mu          0.032468
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.36947258447012, 'aic': -36.73894516894024, 'bic': np.float64(-37.333933529331794)}, 780: {'params': mu          3.671198e-02
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alpha[1]    3.333382e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 38.69998027031238, 'aic': -55.39996054062476, 'bic': np.float64(-55.994948901016315)}, 800: {'params': mu          2.502477e-02
omega       6.069821e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166668e-02
beta[2]     8.166668e-02
beta[3]     8.166668e-02
beta[4]     8.166668e-02
beta[5]     8.166668e-02
beta[6]     8.166668e-02
Name: params, dtype: float64, 'loglikelihood': 37.74214357906252, 'aic': -53.48428715812504, 'bic': np.float64(-54.079275518516596)}, 820: {'params': mu          3.323188e-02
omega       9.410057e-07
alpha[1]    3.333332e-03
alpha[2]    3.333332e-03
alpha[3]    3.333332e-03
beta[1]     8.166664e-02
beta[2]     8.166664e-02
beta[3]     8.166664e-02
beta[4]     8.166664e-02
beta[5]     8.166664e-02
beta[6]     8.166664e-02
Name: params, dtype: float64, 'loglikelihood': 36.21317988881073, 'aic': -50.42635977762146, 'bic': np.float64(-51.02134813801301)}, 840: {'params': mu          0.039971
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.320434722487995, 'aic': -42.64086944497599, 'bic': np.float64(-43.235857805367544)}, 860: {'params': mu          2.572408e-02
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alpha[1]    3.333338e-03
alpha[2]    3.333333e-03
alpha[3]    3.333338e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 39.62403089952844, 'aic': -57.248061799056885, 'bic': np.float64(-57.84305015944844)}, 880: {'params': mu          0.032353
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.435904155780804, 'aic': -44.87180831156161, 'bic': np.float64(-45.46679667195316)}, 900: {'params': mu          0.045219
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 26.50043931942695, 'aic': -31.000878638853898, 'bic': np.float64(-31.59586699924545)}, 920: {'params': mu          4.120654e-02
omega       1.189042e-08
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333338e-03
beta[1]     1.616667e-01
beta[2]     1.616667e-01
beta[3]     1.616667e-01
beta[4]     1.616667e-01
beta[5]     1.616667e-01
beta[6]     1.616667e-01
Name: params, dtype: float64, 'loglikelihood': 40.2362436021338, 'aic': -58.472487204267594, 'bic': np.float64(-59.06747556465915)}, 940: {'params': mu          3.261548e-02
omega       9.198732e-07
alpha[1]    3.333332e-03
alpha[2]    3.333332e-03
alpha[3]    3.333595e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 36.28503664651173, 'aic': -50.570073293023455, 'bic': np.float64(-51.16506165341501)}, 960: {'params': mu          0.034413
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 34.1901834576941, 'aic': -46.380366915388194, 'bic': np.float64(-46.97535527577975)}, 980: {'params': mu          0.025051
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.48674035209252, 'aic': -44.973480704185036, 'bic': np.float64(-45.56846906457659)}, 1000: {'params': mu          0.055566
omega       0.000004
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 31.633923244436613, 'aic': -41.267846488873225, 'bic': np.float64(-41.86283484926478)}, 1020: {'params': mu          0.049825
omega       0.000022
alpha[1]    0.003338
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 25.148943054458694, 'aic': -28.29788610891739, 'bic': np.float64(-28.892874469308943)}, 1040: {'params': mu          0.053167
omega       0.000005
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.62971649115186, 'aic': -39.25943298230372, 'bic': np.float64(-39.854421342695275)}, 1060: {'params': mu          0.035677
omega       0.000009
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.241216341214514, 'aic': -34.48243268242903, 'bic': np.float64(-35.07742104282058)}, 1080: {'params': mu          0.027875
omega       0.000005
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.32188682865082, 'aic': -38.64377365730164, 'bic': np.float64(-39.23876201769319)}, 1100: {'params': mu          0.035623
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.95806464950031, 'aic': -49.916129299000616, 'bic': np.float64(-50.51111765939217)}, 1120: {'params': mu          0.047312
omega       0.000006
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.908983568827274, 'aic': -37.81796713765455, 'bic': np.float64(-38.4129554980461)}, 1140: {'params': mu          0.048907
omega       0.000040
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003341
beta[1]     0.081674
beta[2]     0.081674
beta[3]     0.081674
beta[4]     0.081674
beta[5]     0.081674
beta[6]     0.081673
Name: params, dtype: float64, 'loglikelihood': 23.094165104857005, 'aic': -24.18833020971401, 'bic': np.float64(-24.783318570105564)}, 1160: {'params': mu          0.055016
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 34.714956101744704, 'aic': -47.42991220348941, 'bic': np.float64(-48.02490056388096)}, 1180: {'params': mu          0.034957
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.505131602598944, 'aic': -49.01026320519789, 'bic': np.float64(-49.60525156558944)}, 1200: {'params': mu          0.041619
omega       0.000004
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.307465123649244, 'aic': -40.61493024729849, 'bic': np.float64(-41.20991860769004)}, 1220: {'params': mu          0.033428
omega       0.000004
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 31.46454297309776, 'aic': -40.92908594619552, 'bic': np.float64(-41.524074306587075)}, 1240: {'params': mu          0.022395
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.81569447245127, 'aic': -49.63138894490254, 'bic': np.float64(-50.22637730529409)}, 1260: {'params': mu          0.014235
omega       0.000003
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003334
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.00470324772477, 'aic': -42.00940649544954, 'bic': np.float64(-42.60439485584109)}, 1280: {'params': mu          0.023341
omega       0.000055
alpha[1]    0.003346
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 21.998611177022852, 'aic': -21.997222354045704, 'bic': np.float64(-22.592210714437257)}, 1300: {'params': mu          1.954553e-02
omega       3.204400e-07
alpha[1]    6.666669e-02
alpha[2]    6.666666e-02
alpha[3]    6.666666e-02
beta[1]     5.000000e-02
beta[2]     5.000000e-02
beta[3]     5.000000e-02
beta[4]     5.000000e-02
beta[5]     5.000000e-02
beta[6]     5.000000e-02
Name: params, dtype: float64, 'loglikelihood': 40.03763054185988, 'aic': -58.07526108371977, 'bic': np.float64(-58.67024944411132)}, 1320: {'params': mu          0.033517
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.906175806418535, 'aic': -35.81235161283707, 'bic': np.float64(-36.40733997322862)}, 1340: {'params': mu          1.089894e-02
omega       8.262627e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333461e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 36.66136784373144, 'aic': -51.32273568746288, 'bic': np.float64(-51.917724047854435)}, 1360: {'params': mu          1.697811e-02
omega       2.490244e-08
alpha[1]    3.333336e-03
alpha[2]    3.333335e-03
alpha[3]    3.333334e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 48.92087548448625, 'aic': -75.8417509689725, 'bic': np.float64(-76.43673932936406)}, 1380: {'params': mu          3.440717e-02
omega       6.136373e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 37.703505602120714, 'aic': -53.40701120424143, 'bic': np.float64(-54.00199956463298)}, 1400: {'params': mu          0.041882
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.663463088728946, 'aic': -37.32692617745789, 'bic': np.float64(-37.921914537849446)}, 1420: {'params': mu          0.036046
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.766638775491618, 'aic': -39.533277550983236, 'bic': np.float64(-40.12826591137479)}, 1440: {'params': mu          0.037893
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.296861040877445, 'aic': -34.59372208175489, 'bic': np.float64(-35.188710442146444)}, 1460: {'params': mu          0.188256
omega       0.000001
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 34.59157874103201, 'aic': -47.18315748206402, 'bic': np.float64(-47.77814584245557)}, 1480: {'params': mu          0.029023
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alpha[1]    0.003333
alpha[2]    0.003334
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.53220474511572, 'aic': -45.06440949023144, 'bic': np.float64(-45.659397850622994)}, 1500: {'params': mu          2.101010e-02
omega       3.853653e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     1.150000e-01
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beta[3]     1.150000e-01
beta[4]     1.150000e-01
beta[5]     1.150000e-01
beta[6]     1.150000e-01
Name: params, dtype: float64, 'loglikelihood': 37.530787062770656, 'aic': -53.06157412554131, 'bic': np.float64(-53.65656248593287)}, 1520: {'params': mu          0.029661
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.54464851899189, 'aic': -45.08929703798378, 'bic': np.float64(-45.68428539837534)}, 1540: {'params': mu          2.186034e-02
omega       4.900177e-06
alpha[1]    1.000000e+00
alpha[2]    1.488564e-10
alpha[3]    1.578389e-10
beta[1]     1.184120e-10
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beta[3]     1.179747e-10
beta[4]     3.370054e-10
beta[5]     1.176257e-10
beta[6]     1.173709e-10
Name: params, dtype: float64, 'loglikelihood': 28.127661701111375, 'aic': -34.25532340222275, 'bic': np.float64(-34.850311762614304)}, 1560: {'params': mu          0.017569
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alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.651860962004726, 'aic': -39.30372192400945, 'bic': np.float64(-39.898710284401005)}, 1580: {'params': mu          0.024414
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.447749704190684, 'aic': -44.89549940838137, 'bic': np.float64(-45.49048776877292)}, 1600: {'params': mu          0.049828
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.65116510493582, 'aic': -43.30233020987164, 'bic': np.float64(-43.897318570263195)}, 1620: {'params': mu          2.313002e-02
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alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
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beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 42.1031965595586, 'aic': -62.206393119117195, 'bic': np.float64(-62.80138147950875)}, 1640: {'params': mu          3.085014e-02
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alpha[1]    8.342050e-01
alpha[2]    1.133207e-09
alpha[3]    0.000000e+00
beta[1]     9.601007e-10
beta[2]     8.961915e-10
beta[3]     1.069956e-09
beta[4]     1.657950e-01
beta[5]     9.844862e-10
beta[6]     8.389474e-10
Name: params, dtype: float64, 'loglikelihood': 20.76342884957326, 'aic': -19.526857699146518, 'bic': np.float64(-20.121846059538072)}, 1660: {'params': mu          0.028631
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alpha[1]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.02074457019363, 'aic': -44.041489140387256, 'bic': np.float64(-44.63647750077881)}, 1680: {'params': mu          0.041352
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alpha[1]    0.003334
alpha[2]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.883227915467966, 'aic': -39.76645583093593, 'bic': np.float64(-40.361444191327486)}, 1700: {'params': mu          0.061318
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alpha[1]    0.003334
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alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.096268397535336, 'aic': -34.19253679507067, 'bic': np.float64(-34.78752515546223)}, 1720: {'params': mu          7.556502e-02
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alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166668e-02
beta[2]     8.166668e-02
beta[3]     8.166668e-02
beta[4]     8.166668e-02
beta[5]     8.166668e-02
beta[6]     8.166668e-02
Name: params, dtype: float64, 'loglikelihood': 38.13778374942706, 'aic': -54.275567498854116, 'bic': np.float64(-54.87055585924567)}, 1740: {'params': mu          0.032242
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alpha[1]    0.003333
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beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 27.917628633668656, 'aic': -33.83525726733731, 'bic': np.float64(-34.430245627728866)}, 1760: {'params': mu          0.049081
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
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beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 27.650104689022292, 'aic': -33.300209378044585, 'bic': np.float64(-33.89519773843614)}, 1780: {'params': mu          0.020322
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.403482445028956, 'aic': -44.80696489005791, 'bic': np.float64(-45.401953250449466)}, 1800: {'params': mu          0.029245
omega       0.000046
alpha[1]    0.003348
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081665
Name: params, dtype: float64, 'loglikelihood': 22.607417076796196, 'aic': -23.214834153592392, 'bic': np.float64(-23.809822513983946)}, 1820: {'params': mu          1.064460e-02
omega       3.499858e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333414e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 39.68226968521911, 'aic': -57.36453937043822, 'bic': np.float64(-57.95952773082978)}, 1840: {'params': mu          0.026908
omega       0.000031
alpha[1]    0.003336
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 24.00601466180204, 'aic': -26.012029323604082, 'bic': np.float64(-26.607017683995636)}, 1860: {'params': mu          0.022611
omega       0.000002
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 33.745736151735, 'aic': -45.491472303470005, 'bic': np.float64(-46.08646066386156)}, 1880: {'params': mu          0.017984
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 34.28908630352138, 'aic': -46.57817260704276, 'bic': np.float64(-47.17316096743431)}, 1900: {'params': mu          0.038824
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 31.784555997167484, 'aic': -41.56911199433497, 'bic': np.float64(-42.16410035472652)}, 1920: {'params': mu          0.038409
omega       0.000007
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.034243402109706, 'aic': -36.06848680421941, 'bic': np.float64(-36.663475164610965)}, 1940: {'params': mu          0.063949
omega       0.000009
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.488932200366424, 'aic': -34.97786440073285, 'bic': np.float64(-35.5728527611244)}, 1960: {'params': mu          9.448757e-03
omega       2.384239e-07
alpha[1]    3.333371e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 41.015270592367095, 'aic': -60.03054118473419, 'bic': np.float64(-60.625529545125744)}, 1980: {'params': mu          2.380554e-02
omega       1.108651e-08
alpha[1]    3.333333e-03
alpha[2]    3.333334e-03
alpha[3]    3.333334e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 51.75937064550672, 'aic': -81.51874129101344, 'bic': np.float64(-82.113729651405)}, 2000: {'params': mu          0.019922
omega       0.000001
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 35.73124664062698, 'aic': -49.462493281253956, 'bic': np.float64(-50.05748164164551)}, 2020: {'params': mu          3.228564e-02
omega       2.702095e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 40.587475443344594, 'aic': -59.17495088668919, 'bic': np.float64(-59.76993924708074)}, 2040: {'params': mu          0.033070
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 32.503275792452584, 'aic': -43.00655158490517, 'bic': np.float64(-43.60153994529672)}, 2060: {'params': mu          3.458128e-02
omega       3.193818e-07
alpha[1]    3.333333e-03
alpha[2]    3.333356e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 39.99881211475671, 'aic': -57.99762422951342, 'bic': np.float64(-58.592612589904974)}, 2080: {'params': mu          0.026807
omega       0.000004
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.533874863530222, 'aic': -41.067749727060445, 'bic': np.float64(-41.662738087452)}, 2100: {'params': mu          0.042718
omega       0.000007
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 29.1779246478643, 'aic': -36.3558492957286, 'bic': np.float64(-36.95083765612016)}, 2120: {'params': mu          3.035551e-02
omega       3.823240e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 39.355980661828916, 'aic': -56.71196132365783, 'bic': np.float64(-57.306949684049385)}, 2140: {'params': mu          3.033059e-02
omega       9.395426e-07
alpha[1]    3.333592e-03
alpha[2]    3.333332e-03
alpha[3]    3.333332e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 36.22885490213424, 'aic': -50.457709804268475, 'bic': np.float64(-51.05269816466003)}, 2160: {'params': mu          0.042399
omega       0.000006
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.52621786206894, 'aic': -37.05243572413788, 'bic': np.float64(-37.64742408452943)}, 2180: {'params': mu          0.043877
omega       0.000002
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.8170858957078, 'aic': -43.634171791415596, 'bic': np.float64(-44.22916015180715)}, 2200: {'params': mu          0.050374
omega       0.000004
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.036526760315205, 'aic': -40.07305352063041, 'bic': np.float64(-40.66804188102196)}, 2220: {'params': mu          0.064984
omega       0.000028
alpha[1]    0.003333
alpha[2]    0.003340
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 24.395140285472394, 'aic': -26.790280570944788, 'bic': np.float64(-27.38526893133634)}, 2240: {'params': mu          0.062396
omega       0.000017
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 26.08616259280099, 'aic': -30.172325185601977, 'bic': np.float64(-30.76731354599353)}, 2260: {'params': mu          0.068579
omega       0.000021
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 25.325752644933605, 'aic': -28.65150528986721, 'bic': np.float64(-29.246493650258763)}, 2280: {'params': mu          0.068937
omega       0.000014
alpha[1]    0.003338
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 26.771899904582067, 'aic': -31.543799809164135, 'bic': np.float64(-32.13878816955569)}, 2300: {'params': mu          0.032643
omega       0.000013
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 27.034515271013273, 'aic': -32.069030542026546, 'bic': np.float64(-32.6640189024181)}, 2320: {'params': mu          0.052607
omega       0.000016
alpha[1]    0.003338
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 26.38749779187957, 'aic': -30.774995583759143, 'bic': np.float64(-31.369983944150697)}, 2340: {'params': mu          0.036701
omega       0.000008
alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.518991811021472, 'aic': -35.037983622042944, 'bic': np.float64(-35.6329719824345)}, 2360: {'params': mu          0.039195
omega       0.000016
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 26.37306734893715, 'aic': -30.746134697874297, 'bic': np.float64(-31.34112305826585)}, 2380: {'params': mu          0.059748
omega       0.000099
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003339
beta[1]     0.081674
beta[2]     0.081674
beta[3]     0.081674
beta[4]     0.081674
beta[5]     0.081674
beta[6]     0.081674
Name: params, dtype: float64, 'loglikelihood': 19.9249043503057, 'aic': -17.849808700611398, 'bic': np.float64(-18.44479706100295)}, 2400: {'params': mu          0.035076
omega       0.000007
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.966999381957024, 'aic': -35.93399876391405, 'bic': np.float64(-36.5289871243056)}, 2420: {'params': mu          0.047769
omega       0.000045
alpha[1]    0.003333
alpha[2]    0.003342
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 22.715959044594815, 'aic': -23.43191808918963, 'bic': np.float64(-24.026906449581183)}, 2440: {'params': mu          0.048839
omega       0.000081
alpha[1]    0.003368
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081669
beta[2]     0.081669
beta[3]     0.081669
beta[4]     0.081670
beta[5]     0.081670
beta[6]     0.081669
Name: params, dtype: float64, 'loglikelihood': 20.63356644585481, 'aic': -19.267132891709622, 'bic': np.float64(-19.862121252101176)}, 2460: {'params': mu          0.045623
omega       0.000023
alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 24.97203197836993, 'aic': -27.94406395673986, 'bic': np.float64(-28.539052317131414)}, 2480: {'params': mu          5.170080e-02
omega       8.024413e-07
alpha[1]    3.333333e-03
alpha[2]    3.333526e-03
alpha[3]    3.333333e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 36.773942556321245, 'aic': -51.54788511264249, 'bic': np.float64(-52.142873473034044)}, 2500: {'params': mu          3.613157e-02
omega       7.791620e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166668e-02
beta[2]     8.166668e-02
beta[3]     8.166668e-02
beta[4]     8.166669e-02
beta[5]     8.166669e-02
beta[6]     8.166669e-02
Name: params, dtype: float64, 'loglikelihood': 36.87060749185373, 'aic': -51.741214983707465, 'bic': np.float64(-52.33620334409902)}, 2520: {'params': mu          1.133655e-02
omega       4.088629e-07
alpha[1]    3.333343e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166668e-02
beta[3]     8.166668e-02
beta[4]     8.166668e-02
beta[5]     8.166668e-02
beta[6]     8.166668e-02
Name: params, dtype: float64, 'loglikelihood': 39.12406247391734, 'aic': -56.24812494783468, 'bic': np.float64(-56.843113308226236)}, 2540: {'params': mu          0.031479
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alpha[1]    0.003333
alpha[2]    0.003334
alpha[3]    0.003333
beta[1]     0.081669
beta[2]     0.081669
beta[3]     0.081669
beta[4]     0.081669
beta[5]     0.081669
beta[6]     0.081669
Name: params, dtype: float64, 'loglikelihood': 23.274364028257637, 'aic': -24.548728056515273, 'bic': np.float64(-25.143716416906827)}, 2560: {'params': mu          0.050710
omega       0.000028
alpha[1]    0.003339
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 24.31600355059716, 'aic': -26.63200710119432, 'bic': np.float64(-27.226995461585872)}, 2580: {'params': mu          1.745269e-02
omega       4.103546e-07
alpha[1]    6.666676e-02
alpha[2]    6.666666e-02
alpha[3]    6.666666e-02
beta[1]     4.999999e-02
beta[2]     4.999999e-02
beta[3]     4.999999e-02
beta[4]     4.999999e-02
beta[5]     4.999999e-02
beta[6]     4.999999e-02
Name: params, dtype: float64, 'loglikelihood': 39.15607551348442, 'aic': -56.312151026968834, 'bic': np.float64(-56.90713938736039)}, 2600: {'params': mu          0.018796
omega       0.000008
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 28.775449732295655, 'aic': -35.55089946459131, 'bic': np.float64(-36.145887824982864)}, 2620: {'params': mu          0.066479
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 23.84694311811227, 'aic': -25.693886236224543, 'bic': np.float64(-26.288874596616097)}, 2640: {'params': mu          2.342528e-02
omega       7.308479e-07
alpha[1]    3.333411e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 37.0897377450674, 'aic': -52.179475490134806, 'bic': np.float64(-52.77446385052636)}, 2660: {'params': mu          1.079832e-02
omega       2.285690e-07
alpha[1]    3.333334e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166668e-02
beta[5]     8.166668e-02
beta[6]     8.166668e-02
Name: params, dtype: float64, 'loglikelihood': 41.16245401551281, 'aic': -60.324908031025615, 'bic': np.float64(-60.91989639141717)}, 2680: {'params': mu          0.017037
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.235218162504747, 'aic': -34.470436325009494, 'bic': np.float64(-35.06542468540105)}, 2700: {'params': mu          0.016966
omega       0.000003
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.04547942695521, 'aic': -42.09095885391042, 'bic': np.float64(-42.685947214301976)}, 2720: {'params': mu          0.006252
omega       0.000003
alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 31.820796749509952, 'aic': -41.641593499019905, 'bic': np.float64(-42.23658185941146)}, 2740: {'params': mu          0.011648
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 34.62834949611565, 'aic': -47.25669899223131, 'bic': np.float64(-47.85168735262286)}, 2760: {'params': mu          0.009559
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 34.75373475979795, 'aic': -47.5074695195959, 'bic': np.float64(-48.102457879987455)}, 2780: {'params': mu          5.886377e-02
omega       1.467092e-09
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 58.82466085387776, 'aic': -95.64932170775552, 'bic': np.float64(-96.24431006814707)}, 2800: {'params': mu          0.019675
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 27.755513911000307, 'aic': -33.511027822000614, 'bic': np.float64(-34.10601618239217)}, 2820: {'params': mu          0.057650
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 34.425651925511076, 'aic': -46.85130385102215, 'bic': np.float64(-47.446292211413706)}, 2840: {'params': mu          0.029802
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 27.385909080455658, 'aic': -32.771818160911316, 'bic': np.float64(-33.36680652130287)}, 2860: {'params': mu          1.033890e-02
omega       6.643023e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166668e-02
beta[2]     8.166668e-02
beta[3]     8.166668e-02
beta[4]     8.166668e-02
beta[5]     8.166668e-02
beta[6]     8.166669e-02
Name: params, dtype: float64, 'loglikelihood': 37.421692593877765, 'aic': -52.84338518775553, 'bic': np.float64(-53.438373548147084)}, 2880: {'params': mu          1.680356e-02
omega       1.268494e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333350e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 43.226404087294554, 'aic': -64.45280817458911, 'bic': np.float64(-65.04779653498066)}, 2900: {'params': mu          0.005723
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.60991406595008, 'aic': -49.21982813190016, 'bic': np.float64(-49.81481649229171)}, 2920: {'params': mu          1.030299e-02
omega       4.314952e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 38.93161832431508, 'aic': -55.86323664863016, 'bic': np.float64(-56.45822500902172)}, 2940: {'params': mu          1.861480e-02
omega       8.930102e-07
alpha[1]    3.333441e-03
alpha[2]    3.333332e-03
alpha[3]    3.333332e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 36.41347549724339, 'aic': -50.82695099448678, 'bic': np.float64(-51.42193935487833)}, 2960: {'params': mu          2.196114e-02
omega       4.632949e-07
alpha[1]    3.333343e-02
alpha[2]    3.333333e-02
alpha[3]    3.333333e-02
beta[1]     6.666666e-02
beta[2]     6.666666e-02
beta[3]     6.666666e-02
beta[4]     6.666666e-02
beta[5]     6.666666e-02
beta[6]     6.666666e-02
Name: params, dtype: float64, 'loglikelihood': 38.70430735406727, 'aic': -55.408614708134536, 'bic': np.float64(-56.00360306852609)}, 2980: {'params': mu          0.052938
omega       0.000001
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.245563915169456, 'aic': -48.49112783033891, 'bic': np.float64(-49.086116190730465)}, 3000: {'params': mu          2.931864e-02
omega       6.413947e-07
alpha[1]    3.333358e-03
alpha[2]    3.333347e-03
alpha[3]    3.333333e-03
beta[1]     8.166668e-02
beta[2]     8.166668e-02
beta[3]     8.166668e-02
beta[4]     8.166668e-02
beta[5]     8.166668e-02
beta[6]     8.166668e-02
Name: params, dtype: float64, 'loglikelihood': 37.552503546835666, 'aic': -53.10500709367133, 'bic': np.float64(-53.699995454062886)}, 3020: {'params': mu          3.221179e-02
omega       8.980419e-07
alpha[1]    3.333332e-03
alpha[2]    3.333332e-03
alpha[3]    3.333529e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 36.37174317471944, 'aic': -50.74348634943888, 'bic': np.float64(-51.338474709830436)}, 3040: {'params': mu          0.042605
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 21.455913607987394, 'aic': -20.91182721597479, 'bic': np.float64(-21.506815576366343)}, 3060: {'params': mu          0.038400
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081668
beta[5]     0.081668
beta[6]     0.081668
Name: params, dtype: float64, 'loglikelihood': 24.90032022703604, 'aic': -27.80064045407208, 'bic': np.float64(-28.395628814463635)}, 3080: {'params': mu          0.011289
omega       0.000003
alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.35286142532012, 'aic': -42.70572285064024, 'bic': np.float64(-43.300711211031796)}, 3100: {'params': mu          1.246190e-02
omega       4.299642e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 38.943018380684855, 'aic': -55.88603676136971, 'bic': np.float64(-56.48102512176126)}, 3120: {'params': mu          0.025015
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alpha[1]    0.066668
alpha[2]    0.066666
alpha[3]    0.066666
beta[1]     0.050000
beta[2]     0.050000
beta[3]     0.050000
beta[4]     0.050000
beta[5]     0.050000
beta[6]     0.050000
Name: params, dtype: float64, 'loglikelihood': 26.987521602638722, 'aic': -31.975043205277444, 'bic': np.float64(-32.570031565669)}, 3140: {'params': mu          0.024587
omega       0.000005
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.089205511978534, 'aic': -38.17841102395707, 'bic': np.float64(-38.77339938434862)}, 3160: {'params': mu          0.022189
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alpha[1]    0.003335
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 25.594736336022063, 'aic': -29.189472672044126, 'bic': np.float64(-29.78446103243568)}, 3180: {'params': mu          1.960981e-02
omega       6.781046e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 37.3673909735304, 'aic': -52.734781947060796, 'bic': np.float64(-53.32977030745235)}, 3200: {'params': mu          0.013934
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.13085042349542, 'aic': -40.26170084699084, 'bic': np.float64(-40.856689207382395)}, 3220: {'params': mu          1.033502e-02
omega       2.911703e-07
alpha[1]    3.333345e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 40.31717735483545, 'aic': -58.6343547096709, 'bic': np.float64(-59.229343070062455)}, 3240: {'params': mu          0.023876
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.91544468808412, 'aic': -45.830889376168244, 'bic': np.float64(-46.4258777365598)}, 3260: {'params': mu          2.415329e-02
omega       7.350983e-07
alpha[1]    6.666670e-02
alpha[2]    6.666665e-02
alpha[3]    6.666665e-02
beta[1]     4.999999e-02
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beta[3]     4.999999e-02
beta[4]     4.999999e-02
beta[5]     4.999999e-02
beta[6]     4.999999e-02
Name: params, dtype: float64, 'loglikelihood': 37.16979713984381, 'aic': -52.33959427968762, 'bic': np.float64(-52.93458264007917)}, 3280: {'params': mu          0.038349
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.175850035672156, 'aic': -34.35170007134431, 'bic': np.float64(-34.946688431735865)}, 3300: {'params': mu          2.785451e-02
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alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166668e-02
beta[2]     8.166668e-02
beta[3]     8.166668e-02
beta[4]     8.166668e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 38.971577251901266, 'aic': -55.94315450380253, 'bic': np.float64(-56.538142864194086)}, 3320: {'params': mu          0.046166
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alpha[1]    0.003338
alpha[2]    0.003333
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beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 30.62180190041874, 'aic': -39.24360380083748, 'bic': np.float64(-39.83859216122903)}, 3340: {'params': mu          8.314288e-02
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alpha[1]    3.482041e-01
alpha[2]    2.122243e-16
alpha[3]    9.319904e-19
beta[1]     6.445361e-16
beta[2]     2.297251e-15
beta[3]     1.509987e-15
beta[4]     2.630914e-01
beta[5]     3.887045e-01
beta[6]     3.580469e-15
Name: params, dtype: float64, 'loglikelihood': 13.395486603059185, 'aic': -4.79097320611837, 'bic': np.float64(-5.385961566509923)}, 3360: {'params': mu          4.168133e-02
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alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333426e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 41.61579484596876, 'aic': -61.231589691937515, 'bic': np.float64(-61.82657805232907)}, 3380: {'params': mu          0.022114
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alpha[1]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.58522707937269, 'aic': -41.17045415874538, 'bic': np.float64(-41.76544251913693)}, 3400: {'params': mu          0.030339
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alpha[1]    0.003334
alpha[2]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.3080438994054, 'aic': -34.6160877988108, 'bic': np.float64(-35.21107615920236)}, 3420: {'params': mu          0.028579
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alpha[1]    0.003333
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beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 24.557384664886648, 'aic': -27.114769329773296, 'bic': np.float64(-27.70975769016485)}, 3440: {'params': mu          0.026447
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 27.97675237315611, 'aic': -33.95350474631222, 'bic': np.float64(-34.54849310670377)}, 3460: {'params': mu          0.038928
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alpha[1]    0.066667
alpha[2]    0.066667
alpha[3]    0.066667
beta[1]     0.050000
beta[2]     0.050000
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beta[5]     0.050000
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Name: params, dtype: float64, 'loglikelihood': 31.042859287201246, 'aic': -40.08571857440249, 'bic': np.float64(-40.680706934794046)}, 3480: {'params': mu          1.721059e-02
omega       8.569704e-08
alpha[1]    3.333339e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 44.603665732414136, 'aic': -67.20733146482827, 'bic': np.float64(-67.80231982521983)}, 3500: {'params': mu          0.041341
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.6487073865582, 'aic': -37.2974147731164, 'bic': np.float64(-37.892403133507955)}, 3520: {'params': mu          0.017232
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alpha[1]    0.003334
alpha[2]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.975641153820316, 'aic': -39.95128230764063, 'bic': np.float64(-40.546270668032186)}, 3540: {'params': mu          0.017951
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alpha[1]    0.003334
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.91090159217184, 'aic': -39.82180318434368, 'bic': np.float64(-40.41679154473523)}, 3560: {'params': mu          2.790216e-02
omega       7.981193e-08
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
beta[2]     8.166666e-02
beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 44.84304831994294, 'aic': -67.68609663988587, 'bic': np.float64(-68.28108500027743)}, 3580: {'params': mu          3.588787e-02
omega       8.600668e-08
alpha[1]    3.333330e-03
alpha[2]    3.333330e-03
alpha[3]    3.333573e-03
beta[1]     1.616666e-01
beta[2]     1.616666e-01
beta[3]     1.616666e-01
beta[4]     1.616666e-01
beta[5]     1.616666e-01
beta[6]     1.616666e-01
Name: params, dtype: float64, 'loglikelihood': 33.298802853190985, 'aic': -44.59760570638197, 'bic': np.float64(-45.19259406677352)}, 3600: {'params': mu          2.123429e-02
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alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166668e-02
beta[2]     8.166668e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166668e-02
Name: params, dtype: float64, 'loglikelihood': 40.83867047157469, 'aic': -59.677340943149375, 'bic': np.float64(-60.27232930354093)}, 3620: {'params': mu          7.745735e-02
omega       1.500305e-10
alpha[1]    9.996526e-01
alpha[2]    1.334728e-03
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beta[1]     6.040214e-04
beta[2]     1.002572e-08
beta[3]     4.074899e-04
beta[4]     3.568278e-08
beta[5]     3.575997e-04
beta[6]     5.536856e-04
Name: params, dtype: float64, 'loglikelihood': 26.11335926846638, 'aic': -30.226718536932758, 'bic': np.float64(-30.82170689732431)}, 3640: {'params': mu          0.068875
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alpha[1]    0.003334
alpha[2]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.37931793207284, 'aic': -42.758635864145674, 'bic': np.float64(-43.35362422453723)}, 3660: {'params': mu          6.686305e-02
omega       1.212011e-03
alpha[1]    1.972051e-01
alpha[2]    1.123530e-09
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beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     8.027977e-01
Name: params, dtype: float64, 'loglikelihood': 10.274777683439538, 'aic': 1.4504446331209238, 'bic': np.float64(0.85545627272937)}, 3680: {'params': mu          3.580716e-01
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alpha[1]    1.507507e-03
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     2.168348e-13
beta[2]     2.377957e-13
beta[3]     7.476179e-13
beta[4]     2.588848e-12
beta[5]     3.672951e-12
beta[6]     9.984925e-01
Name: params, dtype: float64, 'loglikelihood': 5.516919331827372, 'aic': 10.966161336345255, 'bic': np.float64(10.371172975953701)}, 3700: {'params': mu          0.030255
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alpha[1]    0.003333
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beta[1]     0.081667
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.866951081814896, 'aic': -49.73390216362979, 'bic': np.float64(-50.32889052402135)}, 3720: {'params': mu          0.058951
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alpha[1]    0.003333
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 34.27125486867236, 'aic': -46.542509737344716, 'bic': np.float64(-47.13749809773627)}, 3740: {'params': mu          0.141973
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alpha[1]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 27.687262978679392, 'aic': -33.374525957358784, 'bic': np.float64(-33.96951431775034)}, 3760: {'params': mu          0.112207
omega       0.000009
alpha[1]    0.003333
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beta[1]     0.161665
beta[2]     0.161665
beta[3]     0.161665
beta[4]     0.161665
beta[5]     0.161665
beta[6]     0.161665
Name: params, dtype: float64, 'loglikelihood': 17.153738919416615, 'aic': -12.307477838833229, 'bic': np.float64(-12.902466199224783)}, 3780: {'params': mu          6.200893e-02
omega       5.105621e-07
alpha[1]    3.333341e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166665e-02
beta[2]     8.166665e-02
beta[3]     8.166665e-02
beta[4]     8.166665e-02
beta[5]     8.166665e-02
beta[6]     8.166665e-02
Name: params, dtype: float64, 'loglikelihood': 38.37150978409067, 'aic': -54.74301956818134, 'bic': np.float64(-55.33800792857289)}, 3800: {'params': mu          5.760531e-02
omega       3.013266e-05
alpha[1]    9.524805e-01
alpha[2]    1.004072e-14
alpha[3]    2.624230e-14
beta[1]     1.001631e-14
beta[2]     2.289050e-14
beta[3]     2.655888e-14
beta[4]     2.429522e-14
beta[5]     4.752450e-02
beta[6]     2.995579e-15
Name: params, dtype: float64, 'loglikelihood': 22.045138697220054, 'aic': -22.090277394440108, 'bic': np.float64(-22.68526575483166)}, 3820: {'params': mu          0.044668
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 34.76239949382692, 'aic': -47.52479898765384, 'bic': np.float64(-48.11978734804539)}, 3840: {'params': mu          0.043141
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 30.44355202297945, 'aic': -38.8871040459589, 'bic': np.float64(-39.48209240635045)}, 3860: {'params': mu          0.025548
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.146528088770346, 'aic': -34.29305617754069, 'bic': np.float64(-34.888044537932245)}, 3880: {'params': mu          2.484305e-02
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alpha[1]    3.333358e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 40.26099250285547, 'aic': -58.521985005710945, 'bic': np.float64(-59.1169733661025)}, 3900: {'params': mu          0.070763
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alpha[1]    0.003337
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081665
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beta[3]     0.081665
beta[4]     0.081665
beta[5]     0.081665
beta[6]     0.081665
Name: params, dtype: float64, 'loglikelihood': 21.41948268977446, 'aic': -20.838965379548917, 'bic': np.float64(-21.43395373994047)}, 3920: {'params': mu          0.030311
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 33.87175085121915, 'aic': -45.743501702438294, 'bic': np.float64(-46.33849006282985)}, 3940: {'params': mu          0.028092
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alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.682387250621577, 'aic': -37.364774501243154, 'bic': np.float64(-37.95976286163471)}, 3960: {'params': mu          0.039297
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alpha[1]    0.003343
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alpha[3]    0.003333
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081668
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 21.42628597884746, 'aic': -20.85257195769492, 'bic': np.float64(-21.447560318086474)}, 3980: {'params': mu          0.118449
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alpha[1]    0.003422
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beta[1]     0.081662
beta[2]     0.081663
beta[3]     0.081663
beta[4]     0.081663
beta[5]     0.081663
beta[6]     0.081663
Name: params, dtype: float64, 'loglikelihood': 18.545604796503177, 'aic': -15.091209593006354, 'bic': np.float64(-15.686197953397908)}, 4000: {'params': mu          0.058034
omega       0.000001
alpha[1]    0.987381
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alpha[3]    0.000031
beta[1]     0.000090
beta[2]     0.000144
beta[3]     0.000146
beta[4]     0.001141
beta[5]     0.002181
beta[6]     0.000146
Name: params, dtype: float64, 'loglikelihood': 17.470530312166826, 'aic': -12.941060624333652, 'bic': np.float64(-13.536048984725205)}, 4020: {'params': mu          0.051020
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beta[1]     0.081667
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.119214655932268, 'aic': -34.238429311864536, 'bic': np.float64(-34.83341767225609)}, 4040: {'params': mu          0.034359
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alpha[1]    0.003333
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beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.159675770701966, 'aic': -34.31935154140393, 'bic': np.float64(-34.914339901795486)}, 4060: {'params': mu          2.769182e-02
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alpha[1]    3.333332e-03
alpha[2]    3.333372e-03
alpha[3]    3.333332e-03
beta[1]     8.166668e-02
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beta[3]     8.166668e-02
beta[4]     8.166668e-02
beta[5]     8.166668e-02
beta[6]     8.166668e-02
Name: params, dtype: float64, 'loglikelihood': 36.10486802164034, 'aic': -50.209736043280685, 'bic': np.float64(-50.80472440367224)}, 4080: {'params': mu          0.014374
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alpha[1]    0.003334
alpha[2]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 28.886065115026714, 'aic': -35.77213023005343, 'bic': np.float64(-36.36711859044498)}, 4100: {'params': mu          8.820277e-03
omega       1.310692e-07
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
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beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 43.109432232582115, 'aic': -64.21886446516423, 'bic': np.float64(-64.81385282555578)}, 4120: {'params': mu          1.661147e-02
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alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166666e-02
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beta[3]     8.166666e-02
beta[4]     8.166666e-02
beta[5]     8.166666e-02
beta[6]     8.166666e-02
Name: params, dtype: float64, 'loglikelihood': 42.11145129352807, 'aic': -62.22290258705614, 'bic': np.float64(-62.817890947447694)}, 4140: {'params': mu          0.017286
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alpha[1]    0.003333
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beta[1]     0.081667
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.413253552080064, 'aic': -48.82650710416013, 'bic': np.float64(-49.42149546455168)}, 4160: {'params': mu          0.029815
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alpha[1]    0.003334
alpha[2]    0.003333
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 31.505695553277757, 'aic': -41.011391106555514, 'bic': np.float64(-41.60637946694707)}, 4180: {'params': mu          2.026255e-02
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alpha[1]    3.333333e-03
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alpha[3]    3.333334e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 49.37254944854308, 'aic': -76.74509889708617, 'bic': np.float64(-77.34008725747772)}, 4200: {'params': mu          0.015528
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alpha[1]    0.003333
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beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.71619802847175, 'aic': -49.4323960569435, 'bic': np.float64(-50.02738441733506)}, 4220: {'params': mu          1.441239e-01
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alpha[2]    8.972722e-10
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beta[1]     3.877656e-09
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beta[3]     8.563764e-09
beta[4]     1.115524e-08
beta[5]     2.506844e-04
beta[6]     5.267958e-09
Name: params, dtype: float64, 'loglikelihood': 20.039237696816468, 'aic': -18.078475393632935, 'bic': np.float64(-18.67346375402449)}, 4240: {'params': mu          0.026777
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alpha[1]    0.003333
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 35.217394648603516, 'aic': -48.43478929720703, 'bic': np.float64(-49.029777657598586)}, 4260: {'params': mu          0.043189
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alpha[1]    0.003333
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.73352504168038, 'aic': -37.46705008336076, 'bic': np.float64(-38.062038443752314)}, 4280: {'params': mu          0.024949
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 32.43763465782471, 'aic': -42.87526931564942, 'bic': np.float64(-43.47025767604097)}, 4300: {'params': mu          0.016988
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alpha[1]    0.003333
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beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 28.48903772091851, 'aic': -34.97807544183702, 'bic': np.float64(-35.573063802228575)}, 4320: {'params': mu          0.016047
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alpha[1]    0.003333
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       6.69677195e-05, 6.70170600e-05, 6.70664005e-05, 6.71157410e-05]), 4820: array([7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
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       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31]), 4840: array([0.0585919 , 0.0585919 , 0.0585919 , 0.0585919 , 0.0585919 ,
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       0.05688442, 0.05692341, 0.05695987, 0.05699072, 0.05701619,
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       0.05712238, 0.05712509, 0.05712734, 0.05712922, 0.05713078,
       0.05713208, 0.05713315, 0.05713405]), 4880: array([0.50244985, 0.52753171, 0.55261358, 0.57769544, 0.60277731,
       0.62785918, 0.65294104, 0.67802291, 0.70310478, 0.72818664,
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       1.00408717, 1.02916904, 1.0542509 , 1.07933277, 1.10441464,
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       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31]), 4920: array([7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
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       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31]), 4960: array([7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31])}}
Resultados Modelo At: {14: {0: {'params': mu          3.159174e-02
omega       2.777969e-11
alpha[1]    1.379583e-01
alpha[2]    5.681109e-08
alpha[3]    7.047699e-01
beta[1]     0.000000e+00
beta[2]     6.664675e-02
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     3.581743e-03
beta[6]     8.710418e-02
Name: params, dtype: float64, 'loglikelihood': 21.578714841115463, 'aic': -21.157429682230926, 'bic': np.float64(-14.127799056463083)}, 20: {'params': mu         -2.277748e-01
omega       4.163559e-06
alpha[1]    9.773580e-01
alpha[2]    6.207596e-07
alpha[3]    0.000000e+00
beta[1]     4.651677e-07
beta[2]     4.658153e-07
beta[3]     0.000000e+00
beta[4]     7.579525e-03
beta[5]     4.658115e-07
beta[6]     5.300928e-07
Name: params, dtype: float64, 'loglikelihood': 23.80219969862695, 'aic': -25.6043993972539, 'bic': np.float64(-18.574768771486056)}, 40: {'params': mu         -4.190423e-01
omega       2.733615e-11
alpha[1]    9.984266e-01
alpha[2]    4.997612e-08
alpha[3]    4.940425e-08
beta[1]     3.748652e-08
beta[2]     3.691088e-08
beta[3]     3.529045e-08
beta[4]     3.539456e-08
beta[5]     3.493274e-08
beta[6]     1.574630e-03
Name: params, dtype: float64, 'loglikelihood': 32.21942697254771, 'aic': -42.43885394509542, 'bic': np.float64(-35.40922331932757)}, 60: {'params': mu         -4.405630e-01
omega       5.572384e-04
alpha[1]    1.000000e+00
alpha[2]    5.289738e-11
alpha[3]    5.509791e-11
beta[1]     3.979917e-11
beta[2]     4.235904e-11
beta[3]     4.238689e-11
beta[4]     4.013590e-11
beta[5]     4.075968e-11
beta[6]     4.194240e-11
Name: params, dtype: float64, 'loglikelihood': 25.171010992721676, 'aic': -28.342021985443353, 'bic': np.float64(-21.31239135967551)}, 80: {'params': mu         -0.392076
omega       0.000032
alpha[1]    0.070797
alpha[2]    0.637884
alpha[3]    0.063967
beta[1]     0.008650
beta[2]     0.008650
beta[3]     0.008650
beta[4]     0.008650
beta[5]     0.008650
beta[6]     0.008650
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Name: params, dtype: float64, 'loglikelihood': 27.700338157974006, 'aic': -33.40067631594801, 'bic': np.float64(-26.371045690180168)}, 400: {'params': mu         -9.439731e-01
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Name: params, dtype: float64, 'loglikelihood': 26.494538172206532, 'aic': -30.989076344413064, 'bic': np.float64(-23.95944571864522)}, 440: {'params': mu         -1.250159
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Name: params, dtype: float64, 'loglikelihood': 36.15393286178708, 'aic': -50.30786572357415, 'bic': np.float64(-43.27823509780631)}, 480: {'params': mu         -1.264943
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Name: params, dtype: float64, 'loglikelihood': 34.35111168970154, 'aic': -46.70222337940308, 'bic': np.float64(-39.672592753635236)}, 580: {'params': mu         -8.431781e-01
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Name: params, dtype: float64, 'loglikelihood': 27.403778239285312, 'aic': -32.807556478570625, 'bic': np.float64(-25.77792585280278)}, 900: {'params': mu         -2.312404e-02
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Name: params, dtype: float64, 'loglikelihood': 23.96935695781628, 'aic': -25.93871391563256, 'bic': np.float64(-18.909083289864718)}, 1760: {'params': mu         -9.580623e-01
omega       2.971037e-11
alpha[1]    9.441013e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     1.863733e-11
beta[2]     0.000000e+00
beta[3]     2.366628e-12
beta[4]     3.463176e-12
beta[5]     2.073555e-12
beta[6]     5.589871e-02
Name: params, dtype: float64, 'loglikelihood': 22.904756478719744, 'aic': -23.809512957439487, 'bic': np.float64(-16.779882331671644)}, 1780: {'params': mu         -1.244881e+00
omega       2.722800e-11
alpha[1]    8.986618e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     1.013399e-01
Name: params, dtype: float64, 'loglikelihood': 23.815694881555828, 'aic': -25.631389763111656, 'bic': np.float64(-18.601759137343812)}, 1800: {'params': mu         -1.349321e+00
omega       2.718297e-06
alpha[1]    1.283423e-09
alpha[2]    2.573696e-01
alpha[3]    1.175745e-09
beta[1]     6.637579e-08
beta[2]     6.632765e-08
beta[3]     3.205463e-01
beta[4]     6.687872e-08
beta[5]     4.220827e-01
beta[6]     9.111501e-07
Name: params, dtype: float64, 'loglikelihood': 36.48328886309418, 'aic': -50.96657772618836, 'bic': np.float64(-43.93694710042052)}, 1820: {'params': mu         -1.585322
omega       0.000065
alpha[1]    0.160018
alpha[2]    0.059999
alpha[3]    0.059999
beta[1]     0.044999
beta[2]     0.044999
beta[3]     0.044999
beta[4]     0.044999
beta[5]     0.044999
beta[6]     0.044999
Name: params, dtype: float64, 'loglikelihood': 42.7827107106732, 'aic': -63.5654214213464, 'bic': np.float64(-56.535790795578556)}, 1840: {'params': mu         -1.628550e+00
omega       1.761145e-12
alpha[1]    1.059926e-04
alpha[2]    1.059888e-04
alpha[3]    1.059895e-04
beta[1]     1.282242e-02
beta[2]     2.966965e-01
beta[3]     2.339560e-01
beta[4]     1.693132e-01
beta[5]     5.197778e-02
beta[6]     2.596902e-03
Name: params, dtype: float64, 'loglikelihood': 41.620488067788294, 'aic': -61.24097613557659, 'bic': np.float64(-54.211345509808744)}, 1860: {'params': mu         -1.682651e+00
omega       1.182143e-04
alpha[1]    9.999998e-01
alpha[2]    5.078656e-08
alpha[3]    5.130149e-08
beta[1]     3.848173e-08
beta[2]     3.902170e-08
beta[3]     3.934850e-08
beta[4]     3.957630e-08
beta[5]     3.914541e-08
beta[6]     3.905290e-08
Name: params, dtype: float64, 'loglikelihood': 31.414136864768253, 'aic': -40.828273729536505, 'bic': np.float64(-33.79864310376866)}, 1880: {'params': mu         -1.685985e+00
omega       3.963387e-05
alpha[1]    1.000000e+00
alpha[2]    3.876683e-11
alpha[3]    1.494974e-10
beta[1]     4.626912e-11
beta[2]     2.221988e-10
beta[3]     3.189028e-10
beta[4]     3.044040e-10
beta[5]     2.737838e-10
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 39.11701434446759, 'aic': -56.23402868893518, 'bic': np.float64(-49.20439806316734)}, 1900: {'params': mu         -1.607026
omega       0.000003
alpha[1]    0.000000
alpha[2]    0.854227
alpha[3]    0.000000
beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.145774
beta[5]     0.000000
beta[6]     0.000000
Name: params, dtype: float64, 'loglikelihood': 31.830751147854986, 'aic': -41.66150229570997, 'bic': np.float64(-34.63187166994213)}, 1920: {'params': mu         -1.693314e+00
omega       3.319520e-11
alpha[1]    8.737294e-01
alpha[2]    8.988058e-07
alpha[3]    8.984574e-07
beta[1]     6.738211e-07
beta[2]     6.734455e-07
beta[3]     6.142116e-02
beta[4]     6.485238e-02
beta[5]     6.745742e-07
beta[6]     6.743287e-07
Name: params, dtype: float64, 'loglikelihood': 23.70555896720561, 'aic': -25.411117934411223, 'bic': np.float64(-18.38148730864338)}, 1940: {'params': mu         -1.498220e+00
omega       1.969142e-03
alpha[1]    1.000000e+00
alpha[2]    4.227643e-14
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 12.566564093269255, 'aic': -3.13312818653851, 'bic': np.float64(3.8965024392293337)}, 1960: {'params': mu         -1.021189
omega       0.000050
alpha[1]    0.003343
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 44.539796244863666, 'aic': -67.07959248972733, 'bic': np.float64(-60.04996186395949)}, 1980: {'params': mu         -9.985037e-01
omega       1.184689e-04
alpha[1]    9.053278e-01
alpha[2]    9.162574e-08
alpha[3]    9.160725e-08
beta[1]     6.870305e-08
beta[2]     6.870230e-08
beta[3]     6.872117e-08
beta[4]     6.865730e-08
beta[5]     6.867367e-08
beta[6]     6.867549e-08
Name: params, dtype: float64, 'loglikelihood': 34.327904157188925, 'aic': -46.65580831437785, 'bic': np.float64(-39.62617768861001)}, 2000: {'params': mu         -0.989780
omega       0.000123
alpha[1]    0.450275
alpha[2]    0.042694
alpha[3]    0.039018
beta[1]     0.029263
beta[2]     0.029263
beta[3]     0.029263
beta[4]     0.029263
beta[5]     0.029263
beta[6]     0.029263
Name: params, dtype: float64, 'loglikelihood': 36.881761232650106, 'aic': -51.76352246530021, 'bic': np.float64(-44.73389183953237)}, 2020: {'params': mu         -9.198668e-01
omega       9.140224e-08
alpha[1]    7.972852e-01
alpha[2]    8.737697e-02
alpha[3]    1.612647e-08
beta[1]     3.903282e-07
beta[2]     3.904502e-07
beta[3]     1.569185e-07
beta[4]     3.903714e-07
beta[5]     3.905117e-07
beta[6]     6.943542e-03
Name: params, dtype: float64, 'loglikelihood': 23.660523599892343, 'aic': -25.321047199784687, 'bic': np.float64(-18.291416574016843)}, 2040: {'params': mu         -1.017422e+00
omega       3.188134e-05
alpha[1]    2.456837e-14
alpha[2]    1.183661e-14
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     1.132309e-01
beta[3]     1.982238e-01
beta[4]     0.000000e+00
beta[5]     6.885453e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 35.07273546259524, 'aic': -48.14547092519048, 'bic': np.float64(-41.115840299422636)}, 2060: {'params': mu         -7.916490e-01
omega       1.159106e-04
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    4.633695e-14
beta[1]     2.643955e-02
beta[2]     5.969538e-02
beta[3]     4.633219e-01
beta[4]     3.004727e-01
beta[5]     1.500704e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 23.992818749598285, 'aic': -25.98563749919657, 'bic': np.float64(-18.956006873428727)}, 2080: {'params': mu         -9.633930e-01
omega       1.666333e-10
alpha[1]    9.073193e-01
alpha[2]    5.014212e-14
alpha[3]    1.053946e-13
beta[1]     9.900423e-14
beta[2]     1.515329e-13
beta[3]     2.992635e-13
beta[4]     1.946293e-13
beta[5]     1.182337e-01
beta[6]     4.343801e-13
Name: params, dtype: float64, 'loglikelihood': 32.50556331172622, 'aic': -43.01112662345244, 'bic': np.float64(-35.9814959976846)}, 2100: {'params': mu         -9.443832e-01
omega       1.020682e-04
alpha[1]    2.096439e-01
alpha[2]    7.903561e-01
alpha[3]    6.348312e-13
beta[1]     5.385156e-13
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     1.222027e-12
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 27.23802537283139, 'aic': -32.47605074566278, 'bic': np.float64(-25.44642011989494)}, 2120: {'params': mu         -8.039104e-01
omega       1.783051e-04
alpha[1]    6.476280e-01
alpha[2]    5.292155e-15
alpha[3]    7.016668e-14
beta[1]     2.442665e-13
beta[2]     2.978068e-13
beta[3]     2.349828e-13
beta[4]     2.720969e-13
beta[5]     3.523720e-01
beta[6]     2.142927e-13
Name: params, dtype: float64, 'loglikelihood': 28.574503647055195, 'aic': -35.14900729411039, 'bic': np.float64(-28.119376668342547)}, 2140: {'params': mu         -0.576262
omega       0.000478
alpha[1]    0.574663
alpha[2]    0.001155
alpha[3]    0.001155
beta[1]     0.028293
beta[2]     0.028293
beta[3]     0.028293
beta[4]     0.028293
beta[5]     0.028293
beta[6]     0.028293
Name: params, dtype: float64, 'loglikelihood': 22.950905328121582, 'aic': -23.901810656243164, 'bic': np.float64(-16.87218003047532)}, 2160: {'params': mu         -6.761730e-01
omega       2.030708e-03
alpha[1]    1.000000e+00
alpha[2]    2.545504e-08
alpha[3]    2.963977e-08
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 17.338582099410118, 'aic': -12.677164198820236, 'bic': np.float64(-5.647533573052392)}, 2180: {'params': mu         -7.970741e-01
omega       1.967482e-03
alpha[1]    4.655129e-01
alpha[2]    5.344871e-01
alpha[3]    4.109163e-16
beta[1]     9.931213e-16
beta[2]     4.374365e-16
beta[3]     7.242808e-16
beta[4]     0.000000e+00
beta[5]     1.024673e-15
beta[6]     1.137674e-15
Name: params, dtype: float64, 'loglikelihood': 13.352323354375523, 'aic': -4.704646708751046, 'bic': np.float64(2.324983917016798)}, 2200: {'params': mu         -0.530550
omega       0.001597
alpha[1]    1.000000
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beta[3]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 13.328375886674634, 'aic': -4.656751773349267, 'bic': np.float64(2.3728788524185767)}, 2220: {'params': mu         -4.130207e-01
omega       1.479872e-03
alpha[1]    6.404986e-01
alpha[2]    8.453330e-04
alpha[3]    5.086631e-13
beta[1]     7.711675e-13
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     3.586561e-01
Name: params, dtype: float64, 'loglikelihood': 13.869843309877808, 'aic': -5.7396866197556164, 'bic': np.float64(1.2899440060122274)}, 2240: {'params': mu         -0.241431
omega       0.000202
alpha[1]    0.880734
alpha[2]    0.119220
alpha[3]    0.000000
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Name: params, dtype: float64, 'loglikelihood': 19.72734369965199, 'aic': -17.454687399303978, 'bic': np.float64(-10.425056773536134)}, 2260: {'params': mu          8.967904e-02
omega       5.998385e-11
alpha[1]    6.830508e-01
alpha[2]    3.894220e-12
alpha[3]    6.631817e-12
beta[1]     1.030117e-11
beta[2]     1.220623e-11
beta[3]     3.185872e-12
beta[4]     3.169492e-01
beta[5]     7.566683e-12
beta[6]     3.498335e-11
Name: params, dtype: float64, 'loglikelihood': 17.38839627258962, 'aic': -12.77679254517924, 'bic': np.float64(-5.747161919411397)}, 2280: {'params': mu          2.530800e-01
omega       1.562558e-10
alpha[1]    8.380057e-01
alpha[2]    8.551112e-10
alpha[3]    8.088574e-10
beta[1]     1.905139e-08
beta[2]     1.900955e-08
beta[3]     0.000000e+00
beta[4]     1.896503e-08
beta[5]     0.000000e+00
beta[6]     1.300645e-01
Name: params, dtype: float64, 'loglikelihood': 13.044577574711537, 'aic': -4.089155149423075, 'bic': np.float64(2.940475476344769)}, 2300: {'params': mu         -2.124763e-01
omega       6.008558e-04
alpha[1]    9.999997e-01
alpha[2]    2.378853e-08
alpha[3]    2.386036e-08
beta[1]     1.784346e-08
beta[2]     1.795094e-08
beta[3]     1.807695e-08
beta[4]     1.805433e-08
beta[5]     1.812670e-08
beta[6]     1.788633e-08
Name: params, dtype: float64, 'loglikelihood': 13.967081246485291, 'aic': -5.934162492970582, 'bic': np.float64(1.0954681327972615)}, 2320: {'params': mu         -5.065069e-01
omega       2.495059e-08
alpha[1]    5.080654e-01
alpha[2]    4.829389e-01
alpha[3]    0.000000e+00
beta[1]     1.112627e-10
beta[2]     6.314626e-11
beta[3]     0.000000e+00
beta[4]     3.076920e-10
beta[5]     9.022990e-03
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 19.920239437741934, 'aic': -17.840478875483868, 'bic': np.float64(-10.810848249716024)}, 2340: {'params': mu         -0.716847
omega       0.000168
alpha[1]    0.186396
alpha[2]    0.294313
alpha[3]    0.255845
beta[1]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 30.970205017808873, 'aic': -39.940410035617745, 'bic': np.float64(-32.9107794098499)}, 2360: {'params': mu         -9.920259e-01
omega       7.768399e-04
alpha[1]    4.683494e-01
alpha[2]    5.316506e-01
alpha[3]    6.461772e-13
beta[1]     0.000000e+00
beta[2]     6.012591e-13
beta[3]     7.524598e-13
beta[4]     7.286469e-13
beta[5]     8.080458e-13
beta[6]     8.222214e-13
Name: params, dtype: float64, 'loglikelihood': 22.9079053828916, 'aic': -23.815810765783198, 'bic': np.float64(-16.786180140015354)}, 2380: {'params': mu         -0.926037
omega       0.000572
alpha[1]    0.990793
alpha[2]    0.000000
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Name: params, dtype: float64, 'loglikelihood': 16.705103487844642, 'aic': -11.410206975689285, 'bic': np.float64(-4.380576349921441)}, 2400: {'params': mu         -0.952033
omega       0.000447
alpha[1]    0.003333
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alpha[3]    0.003333
beta[1]     0.081669
beta[2]     0.081669
beta[3]     0.081670
beta[4]     0.081669
beta[5]     0.081669
beta[6]     0.081670
Name: params, dtype: float64, 'loglikelihood': 29.280754023288413, 'aic': -36.561508046576826, 'bic': np.float64(-29.531877420808982)}, 2420: {'params': mu         -1.347414e+00
omega       5.758633e-04
alpha[1]    9.999984e-01
alpha[2]    1.009379e-07
alpha[3]    1.008143e-07
beta[1]     7.575597e-08
beta[2]     7.564640e-08
beta[3]     7.597233e-08
beta[4]     7.486801e-08
beta[5]     7.540936e-08
beta[6]     7.467642e-08
Name: params, dtype: float64, 'loglikelihood': 20.685893066727274, 'aic': -19.37178613345455, 'bic': np.float64(-12.342155507686705)}, 2440: {'params': mu         -1.451473e+00
omega       9.508790e-11
alpha[1]    9.496573e-01
alpha[2]    6.829122e-12
alpha[3]    3.199910e-11
beta[1]     1.137964e-11
beta[2]     4.982597e-11
beta[3]     4.082516e-11
beta[4]     3.120892e-10
beta[5]     4.173372e-11
beta[6]     5.034272e-02
Name: params, dtype: float64, 'loglikelihood': 15.437949309187447, 'aic': -8.875898618374894, 'bic': np.float64(-1.84626799260705)}, 2460: {'params': mu         -1.349937e+00
omega       5.889117e-05
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    2.013317e-01
beta[1]     8.364768e-14
beta[2]     1.065268e-13
beta[3]     4.577653e-01
beta[4]     4.075583e-14
beta[5]     3.409031e-01
beta[6]     6.915784e-14
Name: params, dtype: float64, 'loglikelihood': 26.802015241587327, 'aic': -31.604030483174654, 'bic': np.float64(-24.57439985740681)}, 2480: {'params': mu         -1.364492e+00
omega       8.783332e-04
alpha[1]    9.762388e-01
alpha[2]    0.000000e+00
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beta[1]     5.417809e-16
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     2.376121e-02
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 14.300614926885292, 'aic': -6.601229853770583, 'bic': np.float64(0.4284007719972607)}, 2500: {'params': mu         -1.698750
omega       0.000552
alpha[1]    0.991874
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Name: params, dtype: float64, 'loglikelihood': 22.55828019387759, 'aic': -23.11656038775518, 'bic': np.float64(-16.086929761987335)}, 2520: {'params': mu         -2.024461
omega       0.000064
alpha[1]    0.999960
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beta[1]     0.000002
beta[2]     0.000002
beta[3]     0.000002
beta[4]     0.000002
beta[5]     0.000002
beta[6]     0.000002
Name: params, dtype: float64, 'loglikelihood': 31.380850435759857, 'aic': -40.761700871519714, 'bic': np.float64(-33.73207024575187)}, 2540: {'params': mu         -2.119505
omega       0.000134
alpha[1]    0.976721
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Name: params, dtype: float64, 'loglikelihood': 23.457985917501542, 'aic': -24.915971835003084, 'bic': np.float64(-17.88634120923524)}, 2560: {'params': mu         -2.046542
omega       0.001247
alpha[1]    0.679496
alpha[2]    0.000013
alpha[3]    0.004450
beta[1]     0.000010
beta[2]     0.044864
beta[3]     0.000010
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Name: params, dtype: float64, 'loglikelihood': 22.64548819118651, 'aic': -23.290976382373017, 'bic': np.float64(-16.261345756605174)}, 2840: {'params': mu         -2.624998e+00
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Name: params, dtype: float64, 'loglikelihood': 40.01767197475858, 'aic': -58.035343949517156, 'bic': np.float64(-51.00571332374931)}, 2900: {'params': mu         -2.933480
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Name: params, dtype: float64, 'loglikelihood': 34.35650728320343, 'aic': -46.713014566406855, 'bic': np.float64(-39.68338394063901)}, 2960: {'params': mu         -3.027949
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Name: params, dtype: float64, 'loglikelihood': 34.42150421616692, 'aic': -46.843008432333846, 'bic': np.float64(-39.813377806566)}, 2980: {'params': mu         -2.988240
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Name: params, dtype: float64, 'loglikelihood': 19.614321712053655, 'aic': -17.22864342410731, 'bic': np.float64(-10.199012798339467)}, 3040: {'params': mu         -3.129119
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Name: params, dtype: float64, 'loglikelihood': 14.544990785823815, 'aic': -7.08998157164763, 'bic': np.float64(-0.06035094587978662)}, 3080: {'params': mu         -3.382989
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Name: params, dtype: float64, 'loglikelihood': 25.799750447901946, 'aic': -29.599500895803892, 'bic': np.float64(-22.56987027003605)}, 3400: {'params': mu         -2.741817
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omega       4.348185e-11
alpha[1]    3.557612e-01
alpha[2]    0.000000e+00
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beta[1]     2.376298e-02
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     5.609812e-01
Name: params, dtype: float64, 'loglikelihood': 42.53967772798124, 'aic': -63.079355455962485, 'bic': np.float64(-48.425105844035244)}, 1760: {'params': mu         -9.666428e-01
omega       1.049713e-03
alpha[1]    4.798501e-01
alpha[2]    5.201499e-01
alpha[3]    9.749485e-12
beta[1]     3.048380e-12
beta[2]     9.382663e-12
beta[3]     1.500771e-11
beta[4]     1.745207e-11
beta[5]     1.981986e-11
beta[6]     2.067771e-11
Name: params, dtype: float64, 'loglikelihood': 25.85974465870287, 'aic': -29.71948931740574, 'bic': np.float64(-15.065239705478497)}, 1780: {'params': mu         -1.326932
omega       0.000080
alpha[1]    0.999872
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alpha[3]    0.000009
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beta[2]     0.000006
beta[3]     0.000006
beta[4]     0.000006
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Name: params, dtype: float64, 'loglikelihood': 57.659014551306946, 'aic': -93.31802910261389, 'bic': np.float64(-78.66377949068665)}, 1800: {'params': mu         -1.350869
omega       0.000320
alpha[1]    1.000000
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Name: params, dtype: float64, 'loglikelihood': 36.70964562945906, 'aic': -51.41929125891812, 'bic': np.float64(-36.76504164699088)}, 1820: {'params': mu         -1.591713
omega       0.000121
alpha[1]    0.548324
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alpha[3]    0.030683
beta[1]     0.023012
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beta[3]     0.023012
beta[4]     0.023012
beta[5]     0.023012
beta[6]     0.023012
Name: params, dtype: float64, 'loglikelihood': 70.53392246929177, 'aic': -119.06784493858353, 'bic': np.float64(-104.41359532665629)}, 1840: {'params': mu         -1.627078
omega       0.000196
alpha[1]    0.986205
alpha[2]    0.000000
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Name: params, dtype: float64, 'loglikelihood': 60.13065340954101, 'aic': -98.26130681908202, 'bic': np.float64(-83.60705720715478)}, 1860: {'params': mu         -1.687175
omega       0.000043
alpha[1]    0.785663
alpha[2]    0.207244
alpha[3]    0.001661
beta[1]     0.002077
beta[2]     0.001669
beta[3]     0.002077
beta[4]     0.000763
beta[5]     0.002015
beta[6]     0.004374
Name: params, dtype: float64, 'loglikelihood': 66.44699183271254, 'aic': -110.89398366542508, 'bic': np.float64(-96.23973405349784)}, 1880: {'params': mu         -1.675685
omega       0.000538
alpha[1]    0.581175
alpha[2]    0.000000
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beta[1]     0.000004
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beta[3]     0.217869
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Name: params, dtype: float64, 'loglikelihood': 50.77180217682007, 'aic': -79.54360435364013, 'bic': np.float64(-64.88935474171289)}, 1900: {'params': mu         -1.612241
omega       0.000466
alpha[1]    0.627270
alpha[2]    0.000000
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beta[1]     0.000000
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beta[3]     0.209130
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Name: params, dtype: float64, 'loglikelihood': 45.930019098630744, 'aic': -69.86003819726149, 'bic': np.float64(-55.20578858533425)}, 1920: {'params': mu         -1.674622
omega       0.001310
alpha[1]    0.934617
alpha[2]    0.000000
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beta[1]     0.000000
beta[2]     0.000000
beta[3]     0.065383
beta[4]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 27.47360189185706, 'aic': -32.94720378371412, 'bic': np.float64(-18.29295417178688)}, 1940: {'params': mu         -1.018625
omega       0.000056
alpha[1]    0.935783
alpha[2]    0.000154
alpha[3]    0.000154
beta[1]     0.000115
beta[2]     0.000115
beta[3]     0.000116
beta[4]     0.000116
beta[5]     0.000116
beta[6]     0.000116
Name: params, dtype: float64, 'loglikelihood': 29.263905758077023, 'aic': -36.527811516154046, 'bic': np.float64(-21.873561904226804)}, 1960: {'params': mu         -1.010098
omega       0.000086
alpha[1]    0.938177
alpha[2]    0.001330
alpha[3]    0.001330
beta[1]     0.000998
beta[2]     0.000998
beta[3]     0.000998
beta[4]     0.000998
beta[5]     0.000998
beta[6]     0.000998
Name: params, dtype: float64, 'loglikelihood': 81.24349274113564, 'aic': -140.48698548227128, 'bic': np.float64(-125.83273587034404)}, 1980: {'params': mu         -9.940807e-01
omega       6.758297e-05
alpha[1]    9.006348e-01
alpha[2]    1.784049e-05
alpha[3]    9.183491e-03
beta[1]     1.928457e-18
beta[2]     2.776945e-19
beta[3]     1.671552e-17
beta[4]     3.259615e-17
beta[5]     2.422951e-17
beta[6]     4.266809e-17
Name: params, dtype: float64, 'loglikelihood': 78.12486946338693, 'aic': -134.24973892677386, 'bic': np.float64(-119.59548931484662)}, 2000: {'params': mu         -1.007698e+00
omega       1.744201e-04
alpha[1]    8.406965e-01
alpha[2]    5.765383e-15
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     1.593035e-01
beta[4]     7.096578e-14
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 59.62007916110782, 'aic': -97.24015832221563, 'bic': np.float64(-82.5859087102884)}, 2020: {'params': mu         -1.008539e+00
omega       4.495556e-04
alpha[1]    1.000000e+00
alpha[2]    6.217249e-18
alpha[3]    2.620126e-18
beta[1]     6.128431e-18
beta[2]     2.398082e-18
beta[3]     9.329385e-06
beta[4]     7.549517e-18
beta[5]     1.776357e-17
beta[6]     1.421085e-17
Name: params, dtype: float64, 'loglikelihood': 44.99237866771929, 'aic': -67.98475733543857, 'bic': np.float64(-53.33050772351133)}, 2040: {'params': mu         -1.005801e+00
omega       3.918438e-04
alpha[1]    9.999996e-01
alpha[2]    0.000000e+00
alpha[3]    3.364519e-07
beta[1]     0.000000e+00
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 37.632690374072, 'aic': -53.265380748144, 'bic': np.float64(-38.611131136216756)}, 2060: {'params': mu         -8.411927e-01
omega       1.217356e-03
alpha[1]    1.000000e+00
alpha[2]    4.849454e-17
alpha[3]    8.615331e-17
beta[1]     4.884981e-17
beta[2]     8.260059e-17
beta[3]     4.893863e-17
beta[4]     7.069900e-17
beta[5]     1.003642e-16
beta[6]     9.716672e-17
Name: params, dtype: float64, 'loglikelihood': 31.586147102854067, 'aic': -41.172294205708134, 'bic': np.float64(-26.518044593780893)}, 2080: {'params': mu         -9.614242e-01
omega       1.436912e-04
alpha[1]    9.999914e-01
alpha[2]    1.673819e-07
alpha[3]    1.617992e-07
beta[1]     1.007863e-06
beta[2]     1.037806e-06
beta[3]     1.014729e-06
beta[4]     1.032097e-06
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beta[6]     1.035114e-06
Name: params, dtype: float64, 'loglikelihood': 53.7254624235148, 'aic': -85.4509248470296, 'bic': np.float64(-70.79667523510236)}, 2100: {'params': mu         -7.918083e-01
omega       1.942740e-04
alpha[1]    1.000000e+00
alpha[2]    4.669687e-10
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beta[1]     4.692190e-10
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beta[3]     1.745053e-09
beta[4]     3.259993e-09
beta[5]     3.164926e-09
beta[6]     4.752021e-09
Name: params, dtype: float64, 'loglikelihood': 36.46205762377307, 'aic': -50.92411524754614, 'bic': np.float64(-36.2698656356189)}, 2120: {'params': mu         -7.038649e-01
omega       4.528392e-04
alpha[1]    7.325581e-01
alpha[2]    3.029804e-07
alpha[3]    2.674422e-01
beta[1]     2.271611e-07
beta[2]     2.271763e-07
beta[3]     2.274011e-07
beta[4]     2.279879e-07
beta[5]     2.282055e-07
beta[6]     2.284929e-07
Name: params, dtype: float64, 'loglikelihood': 35.14866870984772, 'aic': -48.29733741969544, 'bic': np.float64(-33.6430878077682)}, 2140: {'params': mu         -5.867302e-01
omega       5.319304e-04
alpha[1]    1.000000e+00
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beta[4]     2.815518e-12
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Name: params, dtype: float64, 'loglikelihood': 47.27408072723239, 'aic': -72.54816145446478, 'bic': np.float64(-57.893911842537534)}, 2160: {'params': mu         -7.946955e-01
omega       9.940594e-04
alpha[1]    2.726849e-01
alpha[2]    2.961178e-13
alpha[3]    1.600979e-14
beta[1]     5.473016e-01
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beta[3]     2.644845e-13
beta[4]     7.391761e-14
beta[5]     0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 27.00397805548485, 'aic': -32.0079561109697, 'bic': np.float64(-17.35370649904246)}, 2180: {'params': mu         -0.611810
omega       0.000940
alpha[1]    0.840226
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Name: params, dtype: float64, 'loglikelihood': 29.55986874159079, 'aic': -37.11973748318158, 'bic': np.float64(-22.46548787125434)}, 2200: {'params': mu         -3.970919e-01
omega       1.175439e-03
alpha[1]    3.843957e-01
alpha[2]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 29.371121601327737, 'aic': -36.74224320265547, 'bic': np.float64(-22.08799359072823)}, 2220: {'params': mu         -0.430619
omega       0.001879
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Name: params, dtype: float64, 'loglikelihood': 19.40749195537752, 'aic': -16.81498391075504, 'bic': np.float64(-2.1607342988277978)}, 2240: {'params': mu         -2.099566e-01
omega       5.227648e-03
alpha[1]    8.538278e-01
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Name: params, dtype: float64, 'loglikelihood': 17.075888225588134, 'aic': -12.151776451176268, 'bic': np.float64(2.5024731607509736)}, 2260: {'params': mu          8.168621e-02
omega       1.019582e-10
alpha[1]    5.465349e-01
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beta[4]     4.718722e-02
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Name: params, dtype: float64, 'loglikelihood': 30.445702665479644, 'aic': -38.89140533095929, 'bic': np.float64(-24.237155719032046)}, 2280: {'params': mu          0.224681
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Name: params, dtype: float64, 'loglikelihood': 14.081666207610755, 'aic': -6.163332415221511, 'bic': np.float64(8.49091719670573)}, 2300: {'params': mu         -0.401745
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Name: params, dtype: float64, 'loglikelihood': 17.985128102921514, 'aic': -13.970256205843029, 'bic': np.float64(0.6839934060842126)}, 2320: {'params': mu         -6.745621e-01
omega       5.159570e-09
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Name: params, dtype: float64, 'loglikelihood': 32.59316054200653, 'aic': -43.18632108401306, 'bic': np.float64(-28.532071472085818)}, 2340: {'params': mu         -0.719606
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Name: params, dtype: float64, 'loglikelihood': 27.355959230886725, 'aic': -32.71191846177345, 'bic': np.float64(-18.05766884984621)}, 2360: {'params': mu         -1.020002e+00
omega       5.346715e-04
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Name: params, dtype: float64, 'loglikelihood': 34.35413144031143, 'aic': -46.708262880622854, 'bic': np.float64(-32.05401326869561)}, 2380: {'params': mu         -0.925092
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Name: params, dtype: float64, 'loglikelihood': 38.73072241297296, 'aic': -55.46144482594592, 'bic': np.float64(-40.80719521401868)}, 2400: {'params': mu         -0.965944
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Name: params, dtype: float64, 'loglikelihood': 25.946501936272586, 'aic': -29.893003872545172, 'bic': np.float64(-15.238754260617931)}, 2420: {'params': mu         -1.356503e+00
omega       9.252368e-04
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beta[4]     2.848378e-07
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Name: params, dtype: float64, 'loglikelihood': 31.44713347323734, 'aic': -40.89426694647468, 'bic': np.float64(-26.24001733454744)}, 2440: {'params': mu         -1.376193
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Name: params, dtype: float64, 'loglikelihood': 42.09742745720027, 'aic': -62.19485491440054, 'bic': np.float64(-47.540605302473296)}, 2460: {'params': mu         -1.329535e+00
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Name: params, dtype: float64, 'loglikelihood': 41.48383462006008, 'aic': -60.96766924012016, 'bic': np.float64(-46.31341962819292)}, 2480: {'params': mu         -1.468465e+00
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Name: params, dtype: float64, 'loglikelihood': 21.831486121996083, 'aic': -21.662972243992165, 'bic': np.float64(-7.008722632064924)}, 2500: {'params': mu         -1.703824
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Name: params, dtype: float64, 'loglikelihood': 23.537988473787937, 'aic': -25.075976947575874, 'bic': np.float64(-10.421727335648633)}, 2520: {'params': mu         -2.054475
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Name: params, dtype: float64, 'loglikelihood': 53.85655413270944, 'aic': -85.71310826541888, 'bic': np.float64(-71.05885865349164)}, 2540: {'params': mu         -2.146354e+00
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Name: params, dtype: float64, 'loglikelihood': 33.52749196604154, 'aic': -45.054983932083076, 'bic': np.float64(-30.400734320155834)}, 2560: {'params': mu         -2.043493e+00
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Name: params, dtype: float64, 'loglikelihood': 41.87090942748897, 'aic': -61.741818854977936, 'bic': np.float64(-47.087569243050694)}, 2580: {'params': mu         -2.178365
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Name: params, dtype: float64, 'loglikelihood': 59.00381944981886, 'aic': -96.00763889963773, 'bic': np.float64(-81.35338928771048)}, 2980: {'params': mu         -2.875488
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Name: params, dtype: float64, 'loglikelihood': 36.95040308548811, 'aic': -51.900806170976225, 'bic': np.float64(-40.41105935601857)}, 1820: {'params': mu         -1.590145
omega       0.000117
alpha[1]    0.244039
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beta[1]     0.040498
beta[2]     0.040498
beta[3]     0.040498
beta[4]     0.040498
beta[5]     0.040498
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Name: params, dtype: float64, 'loglikelihood': 57.399953775229044, 'aic': -92.79990755045809, 'bic': np.float64(-81.31016073550043)}, 1840: {'params': mu         -1.618425
omega       0.000106
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Name: params, dtype: float64, 'loglikelihood': 49.996339929289284, 'aic': -77.99267985857857, 'bic': np.float64(-66.50293304362091)}, 1860: {'params': mu         -1.699546e+00
omega       1.052186e-11
alpha[1]    0.000000e+00
alpha[2]    7.454073e-07
alpha[3]    7.468300e-07
beta[1]     9.612296e-01
beta[2]     0.000000e+00
beta[3]     9.196451e-06
beta[4]     1.821896e-05
beta[5]     0.000000e+00
beta[6]     3.419705e-06
Name: params, dtype: float64, 'loglikelihood': 42.83056779187761, 'aic': -63.661135583755225, 'bic': np.float64(-52.17138876879757)}, 1880: {'params': mu         -1.683976e+00
omega       1.045546e-04
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     1.080558e-15
beta[2]     1.297718e-14
beta[3]     1.439656e-14
beta[4]     1.948951e-14
beta[5]     1.000000e+00
beta[6]     8.163255e-15
Name: params, dtype: float64, 'loglikelihood': 44.64749036859838, 'aic': -67.29498073719677, 'bic': np.float64(-55.80523392223911)}, 1900: {'params': mu         -1.595532e+00
omega       3.850248e-05
alpha[1]    1.768616e-13
alpha[2]    4.364309e-01
alpha[3]    1.033834e-13
beta[1]     5.200624e-14
beta[2]     6.535006e-14
beta[3]     4.807958e-14
beta[4]     1.177075e-13
beta[5]     5.635691e-01
beta[6]     1.767767e-14
Name: params, dtype: float64, 'loglikelihood': 43.72113910119724, 'aic': -65.44227820239448, 'bic': np.float64(-53.95253138743682)}, 1920: {'params': mu         -1.685336
omega       0.001134
alpha[1]    0.948587
alpha[2]    0.000000
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Name: params, dtype: float64, 'loglikelihood': 25.87364857825222, 'aic': -29.747297156504438, 'bic': np.float64(-18.257550341546782)}, 1940: {'params': mu         -1.490483
omega       0.002407
alpha[1]    1.000000
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Name: params, dtype: float64, 'loglikelihood': 8.247354039659607, 'aic': 5.505291920680786, 'bic': np.float64(16.995038735638442)}, 1960: {'params': mu         -1.013409
omega       0.000065
alpha[1]    0.538978
alpha[2]    0.000000
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Name: params, dtype: float64, 'loglikelihood': 65.45236156961633, 'aic': -108.90472313923266, 'bic': np.float64(-97.414976324275)}, 1980: {'params': mu         -9.955927e-01
omega       7.119389e-05
alpha[1]    8.794932e-01
alpha[2]    0.000000e+00
alpha[3]    1.193921e-02
beta[1]     0.000000e+00
beta[2]     3.251786e-12
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 57.44526940459634, 'aic': -92.89053880919268, 'bic': np.float64(-81.40079199423502)}, 2000: {'params': mu         -1.003706e+00
omega       6.458241e-05
alpha[1]    7.768510e-01
alpha[2]    7.983262e-15
alpha[3]    6.475398e-14
beta[1]     3.417633e-13
beta[2]     2.547562e-13
beta[3]     1.783257e-13
beta[4]     2.231490e-01
beta[5]     3.068364e-13
beta[6]     3.041746e-13
Name: params, dtype: float64, 'loglikelihood': 52.32249999708142, 'aic': -82.64499999416284, 'bic': np.float64(-71.15525317920519)}, 2020: {'params': mu         -9.203579e-01
omega       5.025720e-05
alpha[1]    1.000000e+00
alpha[2]    2.288474e-12
alpha[3]    7.442503e-12
beta[1]     2.322179e-12
beta[2]     7.458061e-12
beta[3]     8.953076e-12
beta[4]     9.929186e-12
beta[5]     1.299471e-11
beta[6]     2.072766e-11
Name: params, dtype: float64, 'loglikelihood': 34.596234046942264, 'aic': -47.19246809388453, 'bic': np.float64(-35.70272127892687)}, 2040: {'params': mu         -1.007031
omega       0.000181
alpha[1]    0.712917
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Name: params, dtype: float64, 'loglikelihood': 38.26816138799706, 'aic': -54.53632277599412, 'bic': np.float64(-43.04657596103647)}, 2060: {'params': mu         -8.267755e-01
omega       1.266751e-03
alpha[1]    9.999971e-01
alpha[2]    2.964628e-07
alpha[3]    2.966846e-07
beta[1]     4.935769e-07
beta[2]     2.225690e-07
beta[3]     2.127253e-06
beta[4]     2.222661e-07
beta[5]     2.224053e-07
beta[6]     2.224289e-07
Name: params, dtype: float64, 'loglikelihood': 27.535324242560986, 'aic': -33.07064848512197, 'bic': np.float64(-21.580901670164316)}, 2080: {'params': mu         -0.991505
omega       0.000045
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Name: params, dtype: float64, 'loglikelihood': 40.94569429928014, 'aic': -59.89138859856028, 'bic': np.float64(-48.40164178360263)}, 2100: {'params': mu         -9.474512e-01
omega       3.038007e-04
alpha[1]    2.946319e-01
alpha[2]    7.053683e-01
alpha[3]    9.637961e-08
beta[1]     7.218843e-08
beta[2]     7.228298e-08
beta[3]     7.227899e-08
beta[4]     7.237394e-08
beta[5]     7.233009e-08
beta[6]     7.241588e-08
Name: params, dtype: float64, 'loglikelihood': 27.29882621499023, 'aic': -32.59765242998046, 'bic': np.float64(-21.1079056150228)}, 2120: {'params': mu         -0.793559
omega       0.000491
alpha[1]    0.890580
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Name: params, dtype: float64, 'loglikelihood': 32.59962913577818, 'aic': -43.19925827155636, 'bic': np.float64(-31.709511456598705)}, 2140: {'params': mu         -0.586483
omega       0.000281
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Name: params, dtype: float64, 'loglikelihood': 39.100407026539806, 'aic': -56.20081405307961, 'bic': np.float64(-44.711067238121956)}, 2160: {'params': mu         -7.081483e-01
omega       2.650192e-03
alpha[1]    8.239438e-01
alpha[2]    3.710901e-08
alpha[3]    3.711964e-08
beta[1]     2.781039e-08
beta[2]     2.782147e-08
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beta[4]     2.784290e-08
beta[5]     2.789409e-08
beta[6]     2.795226e-08
Name: params, dtype: float64, 'loglikelihood': 20.081444452239115, 'aic': -18.16288890447823, 'bic': np.float64(-6.673142089520574)}, 2180: {'params': mu         -6.650223e-01
omega       1.436821e-10
alpha[1]    7.253103e-01
alpha[2]    1.996065e-01
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beta[6]     3.542202e-02
Name: params, dtype: float64, 'loglikelihood': 23.75401860004566, 'aic': -25.508037200091323, 'bic': np.float64(-14.018290385133668)}, 2200: {'params': mu         -4.331728e-01
omega       1.054304e-10
alpha[1]    5.935606e-01
alpha[2]    0.000000e+00
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beta[1]     7.954933e-11
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beta[4]     2.515860e-01
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Name: params, dtype: float64, 'loglikelihood': 21.544114428825647, 'aic': -21.088228857651295, 'bic': np.float64(-9.59848204269364)}, 2220: {'params': mu         -5.477446e-01
omega       2.813655e-03
alpha[1]    9.077308e-01
alpha[2]    6.605142e-02
alpha[3]    2.200968e-11
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beta[4]     1.404077e-10
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beta[6]     2.122449e-10
Name: params, dtype: float64, 'loglikelihood': 15.05825388257769, 'aic': -8.11650776515538, 'bic': np.float64(3.373239049802276)}, 2240: {'params': mu         -0.249588
omega       0.002298
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Name: params, dtype: float64, 'loglikelihood': 18.361004245546148, 'aic': -14.722008491092296, 'bic': np.float64(-3.232261676134641)}, 2260: {'params': mu          8.111818e-02
omega       5.900800e-11
alpha[1]    4.206513e-01
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beta[4]     9.810608e-03
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Name: params, dtype: float64, 'loglikelihood': 25.376978481486322, 'aic': -28.753956962972644, 'bic': np.float64(-17.26421014801499)}, 2280: {'params': mu          0.229461
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Name: params, dtype: float64, 'loglikelihood': 17.059064123048223, 'aic': -12.118128246096447, 'bic': np.float64(-0.6283814311387914)}, 2300: {'params': mu         -0.396284
omega       0.000944
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Name: params, dtype: float64, 'loglikelihood': 17.224246460031008, 'aic': -12.448492920062016, 'bic': np.float64(-0.9587461051043604)}, 2320: {'params': mu         -0.575448
omega       0.000310
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Name: params, dtype: float64, 'loglikelihood': 23.07480158625968, 'aic': -24.149603172519363, 'bic': np.float64(-12.659856357561708)}, 2340: {'params': mu         -7.172712e-01
omega       6.969873e-04
alpha[1]    9.888058e-01
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Name: params, dtype: float64, 'loglikelihood': 28.475652803512578, 'aic': -34.951305607025155, 'bic': np.float64(-23.4615587920675)}, 2360: {'params': mu         -1.032047e+00
omega       3.168500e-04
alpha[1]    6.576254e-01
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Name: params, dtype: float64, 'loglikelihood': 28.35737391561776, 'aic': -34.71474783123552, 'bic': np.float64(-23.225001016277865)}, 2380: {'params': mu         -9.198195e-01
omega       6.247629e-04
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Name: params, dtype: float64, 'loglikelihood': 26.07671277054582, 'aic': -30.153425541091643, 'bic': np.float64(-18.663678726133988)}, 2400: {'params': mu         -9.514208e-01
omega       6.077042e-04
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Name: params, dtype: float64, 'loglikelihood': 30.825227126544537, 'aic': -39.65045425308907, 'bic': np.float64(-28.160707438131418)}, 2420: {'params': mu         -1.354444
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Name: params, dtype: float64, 'loglikelihood': 28.89911149120208, 'aic': -35.79822298240416, 'bic': np.float64(-24.308476167446507)}, 2440: {'params': mu         -1.380914e+00
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Name: params, dtype: float64, 'loglikelihood': 30.53383222457946, 'aic': -39.06766444915892, 'bic': np.float64(-27.577917634201263)}, 2460: {'params': mu         -1.335329
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Name: params, dtype: float64, 'loglikelihood': 31.67140812837353, 'aic': -41.34281625674706, 'bic': np.float64(-29.8530694417894)}, 2480: {'params': mu         -1.449911e+00
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Name: params, dtype: float64, 'loglikelihood': 21.243513289892732, 'aic': -20.487026579785464, 'bic': np.float64(-8.997279764827809)}, 2500: {'params': mu         -1.702442
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Name: params, dtype: float64, 'loglikelihood': 24.989593914092854, 'aic': -27.979187828185708, 'bic': np.float64(-16.489441013228053)}, 2520: {'params': mu         -2.051352
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Name: params, dtype: float64, 'loglikelihood': 45.6681147227843, 'aic': -69.3362294455686, 'bic': np.float64(-57.84648263061095)}, 2540: {'params': mu         -2.153896
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Name: params, dtype: float64, 'loglikelihood': 29.425610025635418, 'aic': -36.851220051270836, 'bic': np.float64(-25.36147323631318)}, 2560: {'params': mu         -2.001738e+00
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Name: params, dtype: float64, 'loglikelihood': 29.620014991247192, 'aic': -37.240029982494384, 'bic': np.float64(-25.75028316753673)}, 2580: {'params': mu         -2.193845
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Name: params, dtype: float64, 'loglikelihood': 32.81706218973074, 'aic': -43.63412437946148, 'bic': np.float64(-32.14437756450383)}, 2600: {'params': mu         -2.28852
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Name: params, dtype: float64, 'loglikelihood': 40.22718808000036, 'aic': -58.45437616000072, 'bic': np.float64(-46.964629345043065)}, 2620: {'params': mu         -2.307000e+00
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Name: params, dtype: float64, 'loglikelihood': 21.426571778044824, 'aic': -20.85314355608965, 'bic': np.float64(-9.363396741131993)}, 2640: {'params': mu         -2.407244
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Name: params, dtype: float64, 'loglikelihood': 47.19778630897165, 'aic': -72.3955726179433, 'bic': np.float64(-60.905825802985646)}, 3020: {'params': mu         -3.019379
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Name: params, dtype: float64, 'loglikelihood': 35.52901549245609, 'aic': -49.05803098491218, 'bic': np.float64(-37.568284169954524)}, 3060: {'params': mu         -3.293966e+00
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Name: params, dtype: float64, 'loglikelihood': 21.678825595048203, 'aic': -21.357651190096405, 'bic': np.float64(-9.86790437513875)}, 3080: {'params': mu         -3.386892e+00
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Name: params, dtype: float64, 'loglikelihood': 57.51128696075393, 'aic': -93.02257392150786, 'bic': np.float64(-81.5328271065502)}, 3120: {'params': mu         -3.444072
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Name: params, dtype: float64, 'loglikelihood': 39.46151249649708, 'aic': -56.92302499299416, 'bic': np.float64(-45.4332781780365)}, 3160: {'params': mu         -3.214521e+00
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Name: params, dtype: float64, 'loglikelihood': 21.775243973935737, 'aic': -21.550487947871474, 'bic': np.float64(-22.145476308263028)}, 180: {'params': mu         -8.575005e-01
omega       3.818421e-05
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alpha[2]    0.000000e+00
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beta[3]     1.594750e-12
beta[4]     0.000000e+00
beta[5]     4.184635e-01
beta[6]     1.846170e-12
Name: params, dtype: float64, 'loglikelihood': 20.854081388251892, 'aic': -19.708162776503784, 'bic': np.float64(-20.303151136895337)}, 200: {'params': mu         -8.785707e-01
omega       1.281598e-04
alpha[1]    1.206159e-01
alpha[2]    0.000000e+00
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beta[1]     0.000000e+00
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
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beta[6]     8.793841e-01
Name: params, dtype: float64, 'loglikelihood': 18.023511575168502, 'aic': -14.047023150337004, 'bic': np.float64(-14.642011510728558)}, 220: {'params': mu         -0.754086
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beta[4]     0.081666
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Name: params, dtype: float64, 'loglikelihood': 23.59984467028611, 'aic': -25.19968934057222, 'bic': np.float64(-25.794677700963774)}, 240: {'params': mu         -0.744622
omega       0.000073
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Name: params, dtype: float64, 'loglikelihood': 20.995563388305538, 'aic': -19.991126776611075, 'bic': np.float64(-20.58611513700263)}, 260: {'params': mu         -0.708453
omega       0.000068
alpha[1]    0.003333
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Name: params, dtype: float64, 'loglikelihood': 21.249648653284467, 'aic': -20.499297306568934, 'bic': np.float64(-21.094285666960488)}, 280: {'params': mu         -8.699279e-01
omega       1.324266e-07
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Name: params, dtype: float64, 'loglikelihood': 19.278947512710587, 'aic': -16.557895025421175, 'bic': np.float64(-17.15288338581273)}, 300: {'params': mu         -0.824439
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Name: params, dtype: float64, 'loglikelihood': 17.663767700987414, 'aic': -13.327535401974828, 'bic': np.float64(-13.922523762366382)}, 320: {'params': mu         -7.563492e-01
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alpha[1]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 18.765271743560348, 'aic': -15.530543487120696, 'bic': np.float64(-16.12553184751225)}, 340: {'params': mu         -0.702783
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Name: params, dtype: float64, 'loglikelihood': 21.25639404448905, 'aic': -20.5127880889781, 'bic': np.float64(-21.107776449369652)}, 360: {'params': mu         -0.784613
omega       0.000139
alpha[1]    0.003333
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Name: params, dtype: float64, 'loglikelihood': 18.734678192426962, 'aic': -15.469356384853924, 'bic': np.float64(-16.064344745245478)}, 380: {'params': mu         -9.869461e-01
omega       3.992215e-09
alpha[1]    2.390581e-06
alpha[2]    2.390488e-06
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beta[1]     6.879046e-01
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beta[4]     5.857252e-05
beta[5]     5.857213e-05
beta[6]     5.857181e-05
Name: params, dtype: float64, 'loglikelihood': 16.423448549929606, 'aic': -10.846897099859213, 'bic': np.float64(-11.441885460250766)}, 400: {'params': mu         -9.600534e-01
omega       2.269167e-11
alpha[1]    6.672538e-12
alpha[2]    6.038470e-01
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beta[1]     1.590131e-10
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beta[4]     1.590399e-10
beta[5]     1.590007e-10
beta[6]     1.588474e-10
Name: params, dtype: float64, 'loglikelihood': 11.662046857458119, 'aic': -1.3240937149162377, 'bic': np.float64(-1.9190820753077915)}, 420: {'params': mu         -0.944898
omega       0.000025
alpha[1]    0.003333
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beta[1]     0.081667
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beta[3]     0.081667
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beta[5]     0.081667
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Name: params, dtype: float64, 'loglikelihood': 24.676356786740854, 'aic': -27.352713573481708, 'bic': np.float64(-27.94770193387326)}, 440: {'params': mu         -1.243828
omega       0.000038
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beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 23.277906211987716, 'aic': -24.555812423975432, 'bic': np.float64(-25.150800784366986)}, 460: {'params': mu         -1.244040e+00
omega       1.808475e-04
alpha[1]    1.000000e+00
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beta[4]     0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 15.277980369069764, 'aic': -8.555960738139529, 'bic': np.float64(-9.150949098531083)}, 480: {'params': mu         -1.263163
omega       0.000030
alpha[1]    0.003333
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beta[1]     0.081666
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beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
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Name: params, dtype: float64, 'loglikelihood': 24.06965133616133, 'aic': -26.139302672322657, 'bic': np.float64(-26.73429103271421)}, 500: {'params': mu         -1.019110e+00
omega       4.015831e-08
alpha[1]    2.111587e-10
alpha[2]    7.079939e-10
alpha[3]    7.493191e-10
beta[1]     6.542177e-01
beta[2]     1.849094e-12
beta[3]     1.641986e-10
beta[4]     2.570018e-10
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beta[6]     4.127049e-10
Name: params, dtype: float64, 'loglikelihood': 7.936532271259255, 'aic': 6.1269354574814905, 'bic': np.float64(5.531947097089937)}, 520: {'params': mu         -1.078402
omega       0.000036
alpha[1]    0.003333
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beta[1]     0.081666
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beta[4]     0.081666
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Name: params, dtype: float64, 'loglikelihood': 23.46989763072856, 'aic': -24.93979526145712, 'bic': np.float64(-25.534783621848675)}, 540: {'params': mu         -1.076932
omega       0.000094
alpha[1]    0.003333
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beta[1]     0.081682
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Name: params, dtype: float64, 'loglikelihood': 20.10147575134011, 'aic': -18.20295150268022, 'bic': np.float64(-18.797939863071775)}, 560: {'params': mu         -1.023822e+00
omega       2.250157e-11
alpha[1]    1.000000e+00
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
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beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 12.601039533063737, 'aic': -3.2020790661274745, 'bic': np.float64(-3.7970674265190283)}, 580: {'params': mu         -0.893558
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alpha[1]    0.003332
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beta[4]     0.161669
beta[5]     0.161669
beta[6]     0.161669
Name: params, dtype: float64, 'loglikelihood': 9.827843579380348, 'aic': 2.3443128412393044, 'bic': np.float64(1.7493244808477506)}, 600: {'params': mu         -8.591413e-01
omega       2.482546e-04
alpha[1]    7.684653e-10
alpha[2]    9.352379e-11
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beta[4]     0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 13.776760443947422, 'aic': -5.5535208878948445, 'bic': np.float64(-6.148509248286398)}, 620: {'params': mu         -9.499022e-01
omega       1.712361e-11
alpha[1]    7.188021e-14
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Name: params, dtype: float64, 'loglikelihood': 12.721501619321776, 'aic': -3.443003238643552, 'bic': np.float64(-4.037991599035106)}, 640: {'params': mu         -9.777230e-01
omega       1.401235e-04
alpha[1]    0.000000e+00
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beta[4]     0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 15.438454808329602, 'aic': -8.876909616659205, 'bic': np.float64(-9.471897977050759)}, 660: {'params': mu         -5.428160e-01
omega       8.913255e-05
alpha[1]    2.002831e-01
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beta[4]     0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 13.162655360844276, 'aic': -4.3253107216885525, 'bic': np.float64(-4.920299082080106)}, 680: {'params': mu         -5.156169e-01
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Name: params, dtype: float64, 'loglikelihood': 8.248178469124854, 'aic': 5.503643061750292, 'bic': np.float64(4.9086547013587385)}, 700: {'params': mu         -0.218443
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alpha[1]    0.003333
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Name: params, dtype: float64, 'loglikelihood': 17.688375052330176, 'aic': -13.376750104660353, 'bic': np.float64(-13.971738465051907)}, 720: {'params': mu         -7.047737e-02
omega       1.161209e-05
alpha[1]    8.661978e-02
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Name: params, dtype: float64, 'loglikelihood': 20.352172821407656, 'aic': -18.704345642815312, 'bic': np.float64(-19.299334003206866)}, 740: {'params': mu         -2.349387e-01
omega       1.731442e-04
alpha[1]    0.000000e+00
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beta[4]     7.259438e-06
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Name: params, dtype: float64, 'loglikelihood': 14.603906867253858, 'aic': -7.207813734507717, 'bic': np.float64(-7.8028020948992705)}, 760: {'params': mu         -2.036868e-01
omega       5.770578e-04
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beta[4]     0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 10.85110854356461, 'aic': 0.2977829128707796, 'bic': np.float64(-0.29720544752077416)}, 780: {'params': mu         -0.235668
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Name: params, dtype: float64, 'loglikelihood': 18.784037004127907, 'aic': -15.568074008255813, 'bic': np.float64(-16.163062368647367)}, 800: {'params': mu         -0.115414
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Name: params, dtype: float64, 'loglikelihood': 18.218414459977172, 'aic': -14.436828919954344, 'bic': np.float64(-15.031817280345898)}, 820: {'params': mu          0.028066
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beta[4]     0.081647
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Name: params, dtype: float64, 'loglikelihood': 13.898856632687394, 'aic': -5.797713265374789, 'bic': np.float64(-6.3927016257663425)}, 840: {'params': mu          2.036162e-01
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beta[4]     1.463541e-06
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Name: params, dtype: float64, 'loglikelihood': 12.465641323660833, 'aic': -2.931282647321666, 'bic': np.float64(-3.5262710077132198)}, 860: {'params': mu          3.487435e-01
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Name: params, dtype: float64, 'loglikelihood': 18.41113408926303, 'aic': -14.822268178526059, 'bic': np.float64(-15.417256538917613)}, 880: {'params': mu          3.194896e-01
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alpha[1]    0.000000e+00
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beta[4]     2.509486e-16
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Name: params, dtype: float64, 'loglikelihood': 15.111187298822715, 'aic': -8.22237459764543, 'bic': np.float64(-8.817362958036984)}, 900: {'params': mu          0.051837
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Name: params, dtype: float64, 'loglikelihood': 10.207779381098092, 'aic': 1.5844412378038157, 'bic': np.float64(0.989452877412262)}, 920: {'params': mu          3.794663e-02
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alpha[1]    2.249023e-14
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beta[4]     6.931437e-15
beta[5]     7.118898e-15
beta[6]     7.551589e-15
Name: params, dtype: float64, 'loglikelihood': 16.550243339851335, 'aic': -11.10048667970267, 'bic': np.float64(-11.695475040094223)}, 940: {'params': mu          1.136705e-01
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alpha[1]    0.000000e+00
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Name: params, dtype: float64, 'loglikelihood': 18.225694116268013, 'aic': -14.451388232536026, 'bic': np.float64(-15.04637659292758)}, 960: {'params': mu         -7.947797e-02
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alpha[1]    3.933697e-12
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beta[6]     1.718222e-11
Name: params, dtype: float64, 'loglikelihood': 15.631435448365187, 'aic': -9.262870896730373, 'bic': np.float64(-9.857859257121927)}, 980: {'params': mu         -2.651723e-01
omega       3.361875e-09
alpha[1]    6.480997e-01
alpha[2]    1.417416e-11
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omega       1.179751e-05
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Name: params, dtype: float64, 'loglikelihood': 12.119586559354271, 'aic': -2.2391731187085426, 'bic': np.float64(-2.8341614791000964)}, 1040: {'params': mu          1.854701e-01
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Name: params, dtype: float64, 'loglikelihood': 10.212073001677625, 'aic': 1.5758539966447493, 'bic': np.float64(0.9808656362531956)}, 1060: {'params': mu          2.974805e-01
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Name: params, dtype: float64, 'loglikelihood': 14.232790089692546, 'aic': -6.465580179385093, 'bic': np.float64(-7.0605685397766464)}, 1080: {'params': mu          0.423026
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Name: params, dtype: float64, 'loglikelihood': 18.305502105795796, 'aic': -14.611004211591592, 'bic': np.float64(-15.205992571983145)}, 1100: {'params': mu          4.318423e-01
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Name: params, dtype: float64, 'loglikelihood': 15.613903606403033, 'aic': -9.227807212806066, 'bic': np.float64(-9.82279557319762)}, 1120: {'params': mu          2.800920e-01
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Name: params, dtype: float64, 'loglikelihood': 8.27572974992491, 'aic': 5.44854050015018, 'bic': np.float64(4.8535521397586265)}, 1140: {'params': mu          4.349224e-02
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Name: params, dtype: float64, 'loglikelihood': 11.58192226725641, 'aic': -1.163844534512819, 'bic': np.float64(-1.7588328949043728)}, 1160: {'params': mu          5.697105e-02
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Name: params, dtype: float64, 'loglikelihood': 13.629458203809497, 'aic': -5.258916407618994, 'bic': np.float64(-5.853904768010548)}, 1180: {'params': mu         -0.268470
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Name: params, dtype: float64, 'loglikelihood': 10.636278842769562, 'aic': 0.7274423144608768, 'bic': np.float64(0.13245395406932303)}, 1200: {'params': mu         -0.571711
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Name: params, dtype: float64, 'loglikelihood': 16.792492266302514, 'aic': -11.584984532605027, 'bic': np.float64(-12.179972892996581)}, 1220: {'params': mu         -0.673017
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Name: params, dtype: float64, 'loglikelihood': 11.913662937763396, 'aic': -1.8273258755267925, 'bic': np.float64(-2.4223142359183463)}, 1240: {'params': mu         -0.899820
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Name: params, dtype: float64, 'loglikelihood': 18.59458927154612, 'aic': -15.18917854309224, 'bic': np.float64(-15.784166903483793)}, 1260: {'params': mu         -1.104910e+00
omega       2.403310e-08
alpha[1]    5.271652e-07
alpha[2]    5.272585e-07
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beta[4]     9.781670e-06
beta[5]     1.270470e-05
beta[6]     1.202551e-05
Name: params, dtype: float64, 'loglikelihood': 17.665925886500524, 'aic': -13.331851773001048, 'bic': np.float64(-13.926840133392602)}, 1280: {'params': mu         -1.091252
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Name: params, dtype: float64, 'loglikelihood': 21.6111580721164, 'aic': -21.2223161442328, 'bic': np.float64(-21.817304504624353)}, 1300: {'params': mu         -1.027215
omega       0.000065
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beta[3]     0.081665
beta[4]     0.081665
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Name: params, dtype: float64, 'loglikelihood': 21.357682865302518, 'aic': -20.715365730605036, 'bic': np.float64(-21.31035409099659)}, 1320: {'params': mu         -1.006628
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Name: params, dtype: float64, 'loglikelihood': 20.536961251647575, 'aic': -19.07392250329515, 'bic': np.float64(-19.668910863686705)}, 1340: {'params': mu         -1.236464e+00
omega       4.826235e-08
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beta[4]     1.493211e-02
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Name: params, dtype: float64, 'loglikelihood': 22.236412374683326, 'aic': -22.47282474936665, 'bic': np.float64(-23.067813109758205)}, 1360: {'params': mu         -1.241044
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Name: params, dtype: float64, 'loglikelihood': 24.52550917707238, 'aic': -27.05101835414476, 'bic': np.float64(-27.646006714536313)}, 1380: {'params': mu         -1.170042e+00
omega       4.395217e-08
alpha[1]    8.721336e-01
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Name: params, dtype: float64, 'loglikelihood': 20.717296582554184, 'aic': -19.434593165108367, 'bic': np.float64(-20.02958152549992)}, 1400: {'params': mu         -1.193502
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Name: params, dtype: float64, 'loglikelihood': 14.52527912276725, 'aic': -7.0505582455345, 'bic': np.float64(-7.645546605926054)}, 1420: {'params': mu         -1.272037e+00
omega       7.564059e-04
alpha[1]    4.909800e-01
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beta[4]     3.218806e-13
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Name: params, dtype: float64, 'loglikelihood': 10.719621355330851, 'aic': 0.5607572893382979, 'bic': np.float64(-0.034231071053255846)}, 1440: {'params': mu         -1.457665e+00
omega       5.383568e-05
alpha[1]    6.839998e-16
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Name: params, dtype: float64, 'loglikelihood': 14.576480836125615, 'aic': -7.15296167225123, 'bic': np.float64(-7.747950032642784)}, 1460: {'params': mu         -1.575346e+00
omega       7.287946e-04
alpha[1]    2.797265e-08
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Name: params, dtype: float64, 'loglikelihood': 9.451934934985145, 'aic': 3.09613013002971, 'bic': np.float64(2.5011417696381564)}, 1480: {'params': mu         -1.039104e+00
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Name: params, dtype: float64, 'loglikelihood': 20.081698226732584, 'aic': -18.163396453465168, 'bic': np.float64(-18.758384813856722)}, 1500: {'params': mu         -8.900141e-01
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Name: params, dtype: float64, 'loglikelihood': 17.93214337956238, 'aic': -13.86428675912476, 'bic': np.float64(-14.459275119516313)}, 1520: {'params': mu         -1.037362
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Name: params, dtype: float64, 'loglikelihood': 17.744577003352198, 'aic': -13.489154006704396, 'bic': np.float64(-14.08414236709595)}, 1540: {'params': mu         -1.203844
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Name: params, dtype: float64, 'loglikelihood': 17.836553560975467, 'aic': -13.673107121950935, 'bic': np.float64(-14.268095482342488)}, 1560: {'params': mu         -1.198896e+00
omega       3.354825e-06
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Name: params, dtype: float64, 'loglikelihood': 22.031940599348687, 'aic': -22.063881198697374, 'bic': np.float64(-22.658869559088927)}, 1580: {'params': mu         -1.166208
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Name: params, dtype: float64, 'loglikelihood': 10.005950509313273, 'aic': 1.9880989813734544, 'bic': np.float64(1.3931106209819006)}, 1600: {'params': mu         -0.939011
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Name: params, dtype: float64, 'loglikelihood': 23.12737774749699, 'aic': -24.25475549499398, 'bic': np.float64(-24.849743855385533)}, 1620: {'params': mu         -1.031011
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Name: params, dtype: float64, 'loglikelihood': 17.617106180432447, 'aic': -13.234212360864895, 'bic': np.float64(-13.829200721256449)}, 1640: {'params': mu         -8.991715e-01
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Name: params, dtype: float64, 'loglikelihood': 6.520169820287387, 'aic': 8.959660359425227, 'bic': np.float64(8.364671999033673)}, 1660: {'params': mu         -7.889378e-01
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Name: params, dtype: float64, 'loglikelihood': 13.424228824400371, 'aic': -4.848457648800743, 'bic': np.float64(-5.4434460091922965)}, 1680: {'params': mu         -7.847977e-01
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Name: params, dtype: float64, 'loglikelihood': 12.12664482048679, 'aic': -2.2532896409735805, 'bic': np.float64(-2.8482780013651343)}, 1700: {'params': mu         -8.172000e-01
omega       1.623447e-04
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Name: params, dtype: float64, 'loglikelihood': 15.625021632328256, 'aic': -9.250043264656512, 'bic': np.float64(-9.845031625048065)}, 1720: {'params': mu         -6.371296e-01
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Name: params, dtype: float64, 'loglikelihood': 12.789824547452126, 'aic': -3.5796490949042514, 'bic': np.float64(-4.174637455295805)}, 1740: {'params': mu         -8.634363e-01
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Name: params, dtype: float64, 'loglikelihood': 11.992063197650555, 'aic': -1.9841263953011108, 'bic': np.float64(-2.5791147556926646)}, 1760: {'params': mu         -8.847912e-01
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Name: params, dtype: float64, 'loglikelihood': 12.18918082258158, 'aic': -2.37836164516316, 'bic': np.float64(-2.973350005554714)}, 1780: {'params': mu         -1.232661e+00
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Name: params, dtype: float64, 'loglikelihood': 17.375187546957587, 'aic': -12.750375093915174, 'bic': np.float64(-13.345363454306728)}, 1800: {'params': mu         -1.348211e+00
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alpha[3]    5.848030e-01
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 19.624167753167566, 'aic': -17.24833550633513, 'bic': np.float64(-17.843323866726685)}, 1820: {'params': mu         -1.581724
omega       0.000125
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081663
beta[2]     0.081663
beta[3]     0.081663
beta[4]     0.081663
beta[5]     0.081663
beta[6]     0.081663
Name: params, dtype: float64, 'loglikelihood': 19.08423497204183, 'aic': -16.16846994408366, 'bic': np.float64(-16.763458304475215)}, 1840: {'params': mu         -1.620140e+00
omega       7.430131e-05
alpha[1]    4.744209e-12
alpha[2]    4.547059e-12
alpha[3]    4.380929e-12
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     1.000000e+00
Name: params, dtype: float64, 'loglikelihood': 18.7527245601365, 'aic': -15.505449120273, 'bic': np.float64(-16.100437480664553)}, 1860: {'params': mu         -1.674360e+00
omega       2.462619e-05
alpha[1]    1.018502e-09
alpha[2]    1.026015e-09
alpha[3]    1.012094e-09
beta[1]     5.419206e-01
beta[2]     7.599804e-02
beta[3]     2.072655e-08
beta[4]     2.074379e-08
beta[5]     2.075748e-08
beta[6]     2.077322e-08
Name: params, dtype: float64, 'loglikelihood': 17.781308610934804, 'aic': -13.562617221869608, 'bic': np.float64(-14.157605582261162)}, 1880: {'params': mu         -1.688713
omega       0.000016
alpha[1]    0.525879
alpha[2]    0.000114
alpha[3]    0.000114
beta[1]     0.002787
beta[2]     0.002787
beta[3]     0.002787
beta[4]     0.002787
beta[5]     0.002787
beta[6]     0.002787
Name: params, dtype: float64, 'loglikelihood': 20.71318909811986, 'aic': -19.426378196239718, 'bic': np.float64(-20.02136655663127)}, 1900: {'params': mu         -1.583258e+00
omega       1.145023e-04
alpha[1]    9.538050e-01
alpha[2]    4.226732e-09
alpha[3]    0.000000e+00
beta[1]     1.084219e-09
beta[2]     9.991360e-10
beta[3]     1.484023e-09
beta[4]     4.619499e-02
beta[5]     1.807553e-09
beta[6]     2.130163e-09
Name: params, dtype: float64, 'loglikelihood': 16.415674056507918, 'aic': -10.831348113015835, 'bic': np.float64(-11.426336473407389)}, 1920: {'params': mu         -1.687910e+00
omega       1.940925e-04
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     8.821572e-01
beta[2]     9.804580e-13
beta[3]     0.000000e+00
beta[4]     4.528910e-14
beta[5]     3.841931e-14
beta[6]     4.883099e-14
Name: params, dtype: float64, 'loglikelihood': 8.07095458428175, 'aic': 5.858090831436499, 'bic': np.float64(5.263102471044945)}, 1940: {'params': mu         -1.520243e+00
omega       4.601005e-06
alpha[1]    2.103173e-05
alpha[2]    3.187417e-18
alpha[3]    1.921793e-02
beta[1]     2.921799e-18
beta[2]     2.619607e-05
beta[3]     3.475973e-04
beta[4]     7.764714e-06
beta[5]     7.837544e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 12.703963799007674, 'aic': -3.4079275980153483, 'bic': np.float64(-4.002915958406902)}, 1960: {'params': mu         -1.014730
omega       0.000027
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 24.51696677593251, 'aic': -27.03393355186502, 'bic': np.float64(-27.628921912256573)}, 1980: {'params': mu         -0.992062
omega       0.000059
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003343
beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 21.73200582933891, 'aic': -21.46401165867782, 'bic': np.float64(-22.059000019069373)}, 2000: {'params': mu         -9.889913e-01
omega       2.816807e-05
alpha[1]    1.000000e+00
alpha[2]    2.480906e-09
alpha[3]    4.340741e-09
beta[1]     2.564281e-09
beta[2]     3.985241e-09
beta[3]     5.611836e-09
beta[4]     8.250153e-10
beta[5]     7.245783e-10
beta[6]     9.160085e-10
Name: params, dtype: float64, 'loglikelihood': 22.496808983509908, 'aic': -22.993617967019816, 'bic': np.float64(-23.58860632741137)}, 2020: {'params': mu         -1.020870e+00
omega       2.731032e-05
alpha[1]    3.079166e-15
alpha[2]    7.839993e-15
alpha[3]    7.888670e-01
beta[1]     2.111330e-01
beta[2]     3.756950e-14
beta[3]     2.465004e-14
beta[4]     3.409365e-15
beta[5]     2.102519e-14
beta[6]     2.047827e-14
Name: params, dtype: float64, 'loglikelihood': 16.19246918862312, 'aic': -10.384938377246243, 'bic': np.float64(-10.979926737637797)}, 2040: {'params': mu         -1.007749e+00
omega       2.579214e-12
alpha[1]    0.000000e+00
alpha[2]    1.262336e-12
alpha[3]    8.654423e-01
beta[1]     1.345577e-01
beta[2]     2.395946e-11
beta[3]     2.391145e-11
beta[4]     2.383638e-11
beta[5]     2.385054e-11
beta[6]     2.385894e-11
Name: params, dtype: float64, 'loglikelihood': 19.820843679379472, 'aic': -17.641687358758944, 'bic': np.float64(-18.236675719150497)}, 2060: {'params': mu         -7.509482e-01
omega       7.526668e-05
alpha[1]    9.699995e-01
alpha[2]    3.001913e-02
alpha[3]    2.086913e-11
beta[1]     7.087921e-12
beta[2]     2.215321e-11
beta[3]     4.310500e-11
beta[4]     4.460466e-11
beta[5]     3.190185e-11
beta[6]     1.176392e-11
Name: params, dtype: float64, 'loglikelihood': 15.031820854700307, 'aic': -8.063641709400613, 'bic': np.float64(-8.658630069792167)}, 2080: {'params': mu         -9.841264e-01
omega       2.053476e-04
alpha[1]    7.794733e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     1.768989e-13
beta[2]     1.773266e-13
beta[3]     1.918198e-13
beta[4]     2.205267e-01
beta[5]     4.169998e-13
beta[6]     2.953373e-13
Name: params, dtype: float64, 'loglikelihood': 14.020524904091618, 'aic': -6.041049808183235, 'bic': np.float64(-6.636038168574789)}, 2100: {'params': mu         -9.247329e-01
omega       9.449109e-06
alpha[1]    9.442513e-01
alpha[2]    5.415028e-08
alpha[3]    9.159215e-08
beta[1]     5.276793e-08
beta[2]     8.756299e-08
beta[3]     1.078469e-07
beta[4]     1.451634e-08
beta[5]     5.575038e-02
beta[6]     2.122420e-08
Name: params, dtype: float64, 'loglikelihood': 13.795501641642728, 'aic': -5.591003283285456, 'bic': np.float64(-6.18599164367701)}, 2120: {'params': mu         -8.117039e-01
omega       1.798627e-07
alpha[1]    5.359315e-01
alpha[2]    3.397432e-15
alpha[3]    1.155173e-14
beta[1]     4.533196e-14
beta[2]     3.874769e-14
beta[3]     7.662416e-14
beta[4]     6.757437e-13
beta[5]     4.640685e-01
beta[6]     4.181184e-12
Name: params, dtype: float64, 'loglikelihood': 16.575943522470418, 'aic': -11.151887044940835, 'bic': np.float64(-11.74687540533239)}, 2140: {'params': mu         -6.344147e-01
omega       1.814585e-04
alpha[1]    3.015724e-16
alpha[2]    0.000000e+00
alpha[3]    2.761612e-01
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     5.560870e-01
beta[4]     0.000000e+00
beta[5]     1.677518e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 12.867531231479411, 'aic': -3.7350624629588225, 'bic': np.float64(-4.330050823350376)}, 2160: {'params': mu         -0.621705
omega       0.001199
alpha[1]    0.003350
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 11.183653656507223, 'aic': -0.36730731301444663, 'bic': np.float64(-0.9622956734060004)}, 2180: {'params': mu         -8.302931e-01
omega       8.530534e-12
alpha[1]    0.000000e+00
alpha[2]    3.722610e-07
alpha[3]    0.000000e+00
beta[1]     1.077576e-07
beta[2]     7.912635e-01
beta[3]     5.604232e-07
beta[4]     5.176275e-07
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 15.211771889938847, 'aic': -8.423543779877694, 'bic': np.float64(-9.018532140269247)}, 2200: {'params': mu         -5.707765e-01
omega       6.576445e-10
alpha[1]    0.000000e+00
alpha[2]    1.844742e-01
alpha[3]    7.273433e-01
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     1.001095e-06
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 10.668918828585948, 'aic': 0.662162342828104, 'bic': np.float64(0.06717398243655026)}, 2220: {'params': mu         -3.834460e-01
omega       1.713762e-05
alpha[1]    4.469022e-11
alpha[2]    3.394893e-04
alpha[3]    9.971728e-01
beta[1]     3.973170e-11
beta[2]     4.156293e-06
beta[3]     2.301205e-11
beta[4]     2.305823e-11
beta[5]     2.305828e-11
beta[6]     2.294537e-11
Name: params, dtype: float64, 'loglikelihood': 12.168876994296632, 'aic': -2.3377539885932634, 'bic': np.float64(-2.9327423489848172)}, 2240: {'params': mu         -3.511578e-01
omega       1.095202e-10
alpha[1]    6.634368e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     3.365632e-01
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 6.183873129317827, 'aic': 9.632253741364346, 'bic': np.float64(9.037265380972793)}, 2260: {'params': mu          2.491444e-02
omega       4.019635e-04
alpha[1]    8.244792e-01
alpha[2]    0.000000e+00
alpha[3]    1.851663e-11
beta[1]     6.924197e-11
beta[2]     5.829356e-10
beta[3]     1.755208e-01
beta[4]     2.627246e-10
beta[5]     6.593606e-11
beta[6]     1.726945e-10
Name: params, dtype: float64, 'loglikelihood': 12.097794579817705, 'aic': -2.1955891596354107, 'bic': np.float64(-2.7905775200269645)}, 2280: {'params': mu          8.267188e-02
omega       1.834198e-03
alpha[1]    1.000000e+00
alpha[2]    2.022567e-14
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     4.497007e-14
beta[5]     3.914800e-13
beta[6]     2.629114e-13
Name: params, dtype: float64, 'loglikelihood': 7.535583166861264, 'aic': 6.928833666277471, 'bic': np.float64(6.333845305885918)}, 2300: {'params': mu         -1.159089e-01
omega       7.783379e-04
alpha[1]    5.062371e-01
alpha[2]    1.540010e-16
alpha[3]    0.000000e+00
beta[1]     2.992297e-16
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     1.618101e-15
beta[5]     4.937629e-01
beta[6]     2.524408e-16
Name: params, dtype: float64, 'loglikelihood': 9.885618686361159, 'aic': 2.228762627277682, 'bic': np.float64(1.6337742668861281)}, 2320: {'params': mu         -0.609001
omega       0.000038
alpha[1]    0.001469
alpha[2]    0.001469
alpha[3]    0.428738
beta[1]     0.071240
beta[2]     0.071240
beta[3]     0.071240
beta[4]     0.071240
beta[5]     0.071240
beta[6]     0.071240
Name: params, dtype: float64, 'loglikelihood': 10.19404152866438, 'aic': 1.6119169426712396, 'bic': np.float64(1.0169285822796859)}, 2340: {'params': mu         -0.697719
omega       0.000445
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003376
beta[1]     0.081653
beta[2]     0.081653
beta[3]     0.081654
beta[4]     0.081653
beta[5]     0.081653
beta[6]     0.081653
Name: params, dtype: float64, 'loglikelihood': 14.637175266577154, 'aic': -7.274350533154308, 'bic': np.float64(-7.869338893545862)}, 2360: {'params': mu         -0.983614
omega       0.000097
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003354
beta[1]     0.081664
beta[2]     0.081664
beta[3]     0.081664
beta[4]     0.081664
beta[5]     0.081664
beta[6]     0.081664
Name: params, dtype: float64, 'loglikelihood': 19.962390707009504, 'aic': -17.92478141401901, 'bic': np.float64(-18.519769774410562)}, 2380: {'params': mu         -1.070683e+00
omega       3.833727e-04
alpha[1]    2.009051e-14
alpha[2]    8.380459e-02
alpha[3]    4.759263e-01
beta[1]     4.402692e-01
beta[2]     0.000000e+00
beta[3]     7.152052e-14
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 6.3638297332001, 'aic': 9.2723405335998, 'bic': np.float64(8.677352173208247)}, 2400: {'params': mu         -9.374214e-01
omega       2.977031e-04
alpha[1]    8.763567e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     4.738836e-10
beta[2]     5.700843e-10
beta[3]     5.705393e-10
beta[4]     1.236433e-01
beta[5]     1.134881e-09
beta[6]     3.086379e-09
Name: params, dtype: float64, 'loglikelihood': 14.623177129175884, 'aic': -7.246354258351769, 'bic': np.float64(-7.841342618743322)}, 2420: {'params': mu         -1.284440e+00
omega       2.072144e-04
alpha[1]    5.907996e-13
alpha[2]    4.506565e-13
alpha[3]    5.370396e-13
beta[1]     9.232607e-01
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     2.931346e-12
beta[5]     8.083553e-12
beta[6]     2.312221e-12
Name: params, dtype: float64, 'loglikelihood': 7.633402218404264, 'aic': 6.733195563191472, 'bic': np.float64(6.138207202799919)}, 2440: {'params': mu         -1.535600
omega       0.003747
alpha[1]    0.003322
alpha[2]    0.003322
alpha[3]    0.004297
beta[1]     0.081748
beta[2]     0.081779
beta[3]     0.081735
beta[4]     0.081717
beta[5]     0.081738
beta[6]     0.081740
Name: params, dtype: float64, 'loglikelihood': 7.398025947977662, 'aic': 7.203948104044676, 'bic': np.float64(6.608959743653122)}, 2460: {'params': mu         -1.354374e+00
omega       1.224057e-11
alpha[1]    1.493735e-09
alpha[2]    0.000000e+00
alpha[3]    8.125883e-01
beta[1]     1.874119e-01
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 14.996874683430832, 'aic': -7.993749366861664, 'bic': np.float64(-8.588737727253218)}, 2480: {'params': mu         -1.298807e+00
omega       2.307671e-11
alpha[1]    4.002268e-15
alpha[2]    7.797792e-01
alpha[3]    2.202208e-01
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     2.515919e-16
beta[4]     3.015637e-16
beta[5]     7.592085e-16
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 11.76871375509465, 'aic': -1.5374275101892998, 'bic': np.float64(-2.1324158705808536)}, 2500: {'params': mu         -1.671916
omega       0.000003
alpha[1]    0.001133
alpha[2]    0.000005
alpha[3]    0.198484
beta[1]     0.502563
beta[2]     0.011941
beta[3]     0.001017
beta[4]     0.000338
beta[5]     0.000802
beta[6]     0.000120
Name: params, dtype: float64, 'loglikelihood': 12.449179194273045, 'aic': -2.8983583885460895, 'bic': np.float64(-3.4933467489376433)}, 2520: {'params': mu         -1.990217
omega       0.000407
alpha[1]    0.003473
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alpha[3]    0.003330
beta[1]     0.081708
beta[2]     0.081710
beta[3]     0.081712
beta[4]     0.081712
beta[5]     0.081712
beta[6]     0.081711
Name: params, dtype: float64, 'loglikelihood': 15.027899822401546, 'aic': -8.055799644803091, 'bic': np.float64(-8.650788005194645)}, 2540: {'params': mu         -2.088278
omega       0.000010
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.161667
beta[2]     0.161667
beta[3]     0.161667
beta[4]     0.161667
beta[5]     0.161667
beta[6]     0.161667
Name: params, dtype: float64, 'loglikelihood': 16.72384825716509, 'aic': -11.447696514330183, 'bic': np.float64(-12.042684874721736)}, 2560: {'params': mu         -2.118844
omega       0.000307
alpha[1]    0.000000
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alpha[3]    0.513906
beta[1]     0.486094
beta[2]     0.000000
beta[3]     0.000000
beta[4]     0.000000
beta[5]     0.000000
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Name: params, dtype: float64, 'loglikelihood': 6.563294786347003, 'aic': 8.873410427305995, 'bic': np.float64(8.278422066914441)}, 2580: {'params': mu         -2.046825e+00
omega       9.542314e-09
alpha[1]    5.604360e-08
alpha[2]    5.804604e-08
alpha[3]    9.980352e-01
beta[1]     0.000000e+00
beta[2]     2.364959e-03
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     8.167981e-05
Name: params, dtype: float64, 'loglikelihood': 20.954078145226713, 'aic': -19.908156290453427, 'bic': np.float64(-20.50314465084498)}, 2600: {'params': mu         -2.171832
omega       0.000143
alpha[1]    0.003350
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081663
beta[2]     0.081663
beta[3]     0.081663
beta[4]     0.081663
beta[5]     0.081663
beta[6]     0.081663
Name: params, dtype: float64, 'loglikelihood': 18.6126491431857, 'aic': -15.225298286371398, 'bic': np.float64(-15.820286646762952)}, 2620: {'params': mu         -2.362109e+00
omega       1.389016e-11
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beta[1]     1.115865e-11
beta[2]     4.053279e-11
beta[3]     2.428090e-01
beta[4]     4.060484e-11
beta[5]     4.055078e-11
beta[6]     4.057180e-11
Name: params, dtype: float64, 'loglikelihood': 13.389605439023889, 'aic': -4.7792108780477776, 'bic': np.float64(-5.374199238439331)}, 2640: {'params': mu         -2.231500
omega       0.000675
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Name: params, dtype: float64, 'loglikelihood': 13.268527977740524, 'aic': -4.537055955481048, 'bic': np.float64(-5.1320443158726015)}, 2660: {'params': mu         -2.420750
omega       0.000035
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beta[5]     0.081667
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Name: params, dtype: float64, 'loglikelihood': 23.56484603941684, 'aic': -25.129692078833678, 'bic': np.float64(-25.72468043922523)}, 2680: {'params': mu         -2.459515e+00
omega       1.317250e-04
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alpha[2]    0.000000e+00
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beta[6]     2.095986e-12
Name: params, dtype: float64, 'loglikelihood': 17.25491502018325, 'aic': -12.509830040366502, 'bic': np.float64(-13.104818400758056)}, 2700: {'params': mu         -2.521755e+00
omega       1.419516e-04
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alpha[2]    0.000000e+00
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beta[4]     1.438363e-10
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beta[6]     1.000000e+00
Name: params, dtype: float64, 'loglikelihood': 15.458601468132718, 'aic': -8.917202936265436, 'bic': np.float64(-9.51219129665699)}, 2720: {'params': mu         -2.627185
omega       0.000030
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beta[6]     0.001728
Name: params, dtype: float64, 'loglikelihood': 20.69431357186364, 'aic': -19.388627143727277, 'bic': np.float64(-19.98361550411883)}, 2740: {'params': mu         -2.642244
omega       0.000025
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 24.802374851314454, 'aic': -27.604749702628908, 'bic': np.float64(-28.19973806302046)}, 2760: {'params': mu         -2.695525
omega       0.000012
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beta[3]     0.081666
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Name: params, dtype: float64, 'loglikelihood': 27.211986464555412, 'aic': -32.423972929110825, 'bic': np.float64(-33.01896128950238)}, 2780: {'params': mu         -2.670884
omega       0.000006
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 29.8946032912005, 'aic': -37.789206582401, 'bic': np.float64(-38.384194942792554)}, 2800: {'params': mu         -2.526848
omega       0.000080
alpha[1]    0.003333
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beta[3]     0.081665
beta[4]     0.081665
beta[5]     0.081665
beta[6]     0.081665
Name: params, dtype: float64, 'loglikelihood': 20.65624906603929, 'aic': -19.31249813207858, 'bic': np.float64(-19.907486492470134)}, 2820: {'params': mu         -2.524320e+00
omega       3.521633e-07
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    7.593626e-01
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 15.316164134707968, 'aic': -8.632328269415936, 'bic': np.float64(-9.22731662980749)}, 2840: {'params': mu         -2.623451
omega       0.000121
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beta[4]     0.003149
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Name: params, dtype: float64, 'loglikelihood': 11.627138200004104, 'aic': -1.2542764000082087, 'bic': np.float64(-1.8492647603997625)}, 2860: {'params': mu         -2.881000
omega       0.000048
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beta[3]     0.081669
beta[4]     0.081669
beta[5]     0.081669
beta[6]     0.081670
Name: params, dtype: float64, 'loglikelihood': 22.48735214654108, 'aic': -22.974704293082162, 'bic': np.float64(-23.569692653473716)}, 2880: {'params': mu         -2.869162
omega       0.000030
alpha[1]    0.003333
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beta[3]     0.081659
beta[4]     0.081659
beta[5]     0.081659
beta[6]     0.081659
Name: params, dtype: float64, 'loglikelihood': 24.150349128902434, 'aic': -26.300698257804868, 'bic': np.float64(-26.89568661819642)}, 2900: {'params': mu         -2.931128
omega       0.000019
alpha[1]    0.003334
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beta[1]     0.081667
beta[2]     0.081667
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 25.61551755968048, 'aic': -29.23103511936096, 'bic': np.float64(-29.826023479752514)}, 2920: {'params': mu         -2.949277
omega       0.000024
alpha[1]    0.003333
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beta[1]     0.081668
beta[2]     0.081668
beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081668
Name: params, dtype: float64, 'loglikelihood': 24.845689512592273, 'aic': -27.691379025184546, 'bic': np.float64(-28.2863673855761)}, 2940: {'params': mu         -2.922612e+00
omega       3.055031e-07
alpha[1]    7.592042e-01
alpha[2]    1.333291e-05
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beta[1]     1.359794e-03
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beta[3]     1.435448e-01
beta[4]     5.170205e-03
beta[5]     3.264290e-04
beta[6]     1.272505e-03
Name: params, dtype: float64, 'loglikelihood': 14.877897238468659, 'aic': -7.755794476937318, 'bic': np.float64(-8.350782837328872)}, 2960: {'params': mu         -3.023695e+00
omega       5.110388e-05
alpha[1]    1.689155e-06
alpha[2]    1.691767e-06
alpha[3]    1.690923e-06
beta[1]     7.557407e-01
beta[2]     1.968425e-17
beta[3]     3.145262e-17
beta[4]     3.291811e-17
beta[5]     5.729783e-06
beta[6]     1.594999e-04
Name: params, dtype: float64, 'loglikelihood': 16.035004667431963, 'aic': -10.070009334863926, 'bic': np.float64(-10.66499769525548)}, 2980: {'params': mu         -2.982298e+00
omega       9.417472e-05
alpha[1]    8.083858e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     0.000000e+00
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beta[3]     1.157723e-14
beta[4]     0.000000e+00
beta[5]     1.916142e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 14.804258061695238, 'aic': -7.608516123390476, 'bic': np.float64(-8.20350448378203)}, 3000: {'params': mu         -2.876698
omega       0.000014
alpha[1]    0.003333
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beta[1]     0.081667
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beta[3]     0.081667
beta[4]     0.081667
beta[5]     0.081667
beta[6]     0.081667
Name: params, dtype: float64, 'loglikelihood': 26.79361337966109, 'aic': -31.587226759322178, 'bic': np.float64(-32.18221511971373)}, 3020: {'params': mu         -2.845249e+00
omega       1.702224e-04
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     8.294447e-11
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beta[3]     9.421526e-11
beta[4]     8.724306e-10
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beta[6]     1.000000e+00
Name: params, dtype: float64, 'loglikelihood': 14.299301268964637, 'aic': -6.598602537929274, 'bic': np.float64(-7.193590898320828)}, 3040: {'params': mu         -3.139976
omega       0.000052
alpha[1]    0.000219
alpha[2]    0.000219
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beta[3]     0.005368
beta[4]     0.005363
beta[5]     0.005363
beta[6]     0.005363
Name: params, dtype: float64, 'loglikelihood': 15.54050623397004, 'aic': -9.08101246794008, 'bic': np.float64(-9.676000828331635)}, 3060: {'params': mu         -2.994939e+00
omega       1.357536e-03
alpha[1]    3.797753e-01
alpha[2]    3.560489e-15
alpha[3]    6.202247e-01
beta[1]     1.293019e-15
beta[2]     3.476799e-15
beta[3]     2.350107e-15
beta[4]     8.538380e-16
beta[5]     2.163238e-15
beta[6]     1.631768e-15
Name: params, dtype: float64, 'loglikelihood': 7.578680939000272, 'aic': 6.842638121999457, 'bic': np.float64(6.247649761607903)}, 3080: {'params': mu         -3.353449
omega       0.000002
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Name: params, dtype: float64, 'loglikelihood': 15.037288718093826, 'aic': -8.074577436187653, 'bic': np.float64(-8.669565796579207)}, 3100: {'params': mu         -3.436796e+00
omega       3.185209e-05
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
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beta[1]     1.501256e-06
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beta[3]     3.744367e-08
beta[4]     1.014949e-06
beta[5]     2.574763e-05
beta[6]     9.999716e-01
Name: params, dtype: float64, 'loglikelihood': 20.949501988991912, 'aic': -19.899003977983824, 'bic': np.float64(-20.493992338375378)}, 3120: {'params': mu         -3.433368
omega       0.000248
alpha[1]    0.003333
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beta[1]     0.081659
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beta[3]     0.081659
beta[4]     0.081659
beta[5]     0.081659
beta[6]     0.081659
Name: params, dtype: float64, 'loglikelihood': 16.696688617403183, 'aic': -11.393377234806366, 'bic': np.float64(-11.98836559519792)}, 3140: {'params': mu         -3.306459
omega       0.000061
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Name: params, dtype: float64, 'loglikelihood': 16.060635877515537, 'aic': -10.121271755031074, 'bic': np.float64(-10.716260115422628)}, 3160: {'params': mu         -3.200201e+00
omega       1.082353e-04
alpha[1]    1.567326e-09
alpha[2]    1.600040e-09
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beta[1]     0.000000e+00
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beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     1.000000e+00
Name: params, dtype: float64, 'loglikelihood': 17.85552240001364, 'aic': -13.711044800027281, 'bic': np.float64(-14.306033160418835)}, 3180: {'params': mu         -3.270041e+00
omega       4.523025e-05
alpha[1]    1.000000e+00
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alpha[3]    5.355630e-10
beta[1]     0.000000e+00
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beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 19.719161066646237, 'aic': -17.438322133292473, 'bic': np.float64(-18.033310493684027)}, 3200: {'params': mu         -3.351583e+00
omega       1.624382e-04
alpha[1]    9.999668e-01
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beta[3]     2.194434e-06
beta[4]     8.147617e-07
beta[5]     2.598107e-06
beta[6]     1.002301e-06
Name: params, dtype: float64, 'loglikelihood': 15.974670188340824, 'aic': -9.949340376681647, 'bic': np.float64(-10.5443287370732)}, 3220: {'params': mu         -3.383087
omega       0.000040
alpha[1]    0.003333
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beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 23.08881837748197, 'aic': -24.17763675496394, 'bic': np.float64(-24.772625115355495)}, 3240: {'params': mu         -3.377926
omega       0.000145
alpha[1]    0.003333
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beta[3]     0.081675
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beta[5]     0.081675
beta[6]     0.081675
Name: params, dtype: float64, 'loglikelihood': 18.57495468525361, 'aic': -15.149909370507217, 'bic': np.float64(-15.74489773089877)}, 3260: {'params': mu         -3.436088e+00
omega       2.573972e-05
alpha[1]    1.244364e-11
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beta[4]     3.261936e-10
beta[5]     2.869857e-10
beta[6]     2.868630e-10
Name: params, dtype: float64, 'loglikelihood': 21.79287034981082, 'aic': -21.58574069962164, 'bic': np.float64(-22.180729060013192)}, 3280: {'params': mu         -3.332346
omega       0.000072
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beta[3]     0.081665
beta[4]     0.081665
beta[5]     0.081665
beta[6]     0.081665
Name: params, dtype: float64, 'loglikelihood': 21.024461797302017, 'aic': -20.048923594604034, 'bic': np.float64(-20.643911954995588)}, 3300: {'params': mu         -3.191787e+00
omega       9.799756e-12
alpha[1]    2.740512e-06
alpha[2]    0.000000e+00
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beta[1]     9.095866e-01
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beta[4]     1.519072e-06
beta[5]     2.249426e-06
beta[6]     2.791651e-06
Name: params, dtype: float64, 'loglikelihood': 14.460813668598933, 'aic': -6.921627337197865, 'bic': np.float64(-7.516615697589419)}, 3320: {'params': mu         -3.337278e+00
omega       2.301385e-04
alpha[1]    0.000000e+00
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beta[1]     6.204260e-08
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beta[3]     1.214791e-07
beta[4]     3.022272e-06
beta[5]     9.999968e-01
beta[6]     3.836740e-09
Name: params, dtype: float64, 'loglikelihood': 13.888968081076618, 'aic': -5.777936162153235, 'bic': np.float64(-6.372924522544789)}, 3340: {'params': mu         -3.284656e+00
omega       3.311280e-11
alpha[1]    8.677810e-14
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Name: params, dtype: float64, 'loglikelihood': 10.191783897984248, 'aic': 1.6164322040315042, 'bic': np.float64(1.0214438436399504)}, 3360: {'params': mu         -3.051242e+00
omega       5.290229e-06
alpha[1]    0.000000e+00
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beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 15.10705212615539, 'aic': -8.21410425231078, 'bic': np.float64(-8.809092612702333)}, 3380: {'params': mu         -2.888599
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Name: params, dtype: float64, 'loglikelihood': 14.448883078279039, 'aic': -6.8977661565580775, 'bic': np.float64(-7.492754516949631)}, 3400: {'params': mu         -2.741911e+00
omega       2.543254e-05
alpha[1]    8.926866e-01
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beta[4]     1.073134e-01
beta[5]     2.827163e-16
beta[6]     2.255141e-16
Name: params, dtype: float64, 'loglikelihood': 21.25923779803976, 'aic': -20.51847559607952, 'bic': np.float64(-21.113463956471072)}, 3420: {'params': mu         -2.780878
omega       0.000488
alpha[1]    0.003333
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beta[3]     0.081647
beta[4]     0.081647
beta[5]     0.081647
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Name: params, dtype: float64, 'loglikelihood': 14.326440308859027, 'aic': -6.652880617718054, 'bic': np.float64(-7.247868978109608)}, 3440: {'params': mu         -2.690140
omega       0.000058
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Name: params, dtype: float64, 'loglikelihood': 21.841337746395553, 'aic': -21.682675492791105, 'bic': np.float64(-22.27766385318266)}, 3580: {'params': mu         -2.135336e+00
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Name: params, dtype: float64, 'loglikelihood': 11.086776747205414, 'aic': -0.1735534944108288, 'bic': np.float64(-0.7685418548023826)}, 3600: {'params': mu         -2.479470e+00
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Name: params, dtype: float64, 'loglikelihood': 19.487289135919216, 'aic': -16.974578271838432, 'bic': np.float64(-17.569566632229986)}, 3620: {'params': mu         -2.361496e+00
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Name: params, dtype: float64, 'loglikelihood': 15.951487773886718, 'aic': -9.902975547773437, 'bic': np.float64(-10.49796390816499)}, 3640: {'params': mu         -2.419684e+00
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Name: params, dtype: float64, 'loglikelihood': 15.847568549297968, 'aic': -9.695137098595936, 'bic': np.float64(-10.29012545898749)}, 3660: {'params': mu         -2.065409
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Name: params, dtype: float64, 'loglikelihood': 23.15039111744883, 'aic': -24.30078223489766, 'bic': np.float64(-24.895770595289214)}, 3680: {'params': mu         -2.058220e+00
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Name: params, dtype: float64, 'loglikelihood': -5.7630585333345925, 'aic': 33.52611706666919, 'bic': np.float64(32.93112870627763)}, 3700: {'params': mu          0.185745
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Name: params, dtype: float64, 'loglikelihood': 22.581094837192147, 'aic': -23.162189674384294, 'bic': np.float64(-23.757178034775848)}, 3720: {'params': mu          1.972300e-01
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Name: params, dtype: float64, 'loglikelihood': 20.64466808577313, 'aic': -19.28933617154626, 'bic': np.float64(-19.884324531937814)}, 3740: {'params': mu         -8.933330e-02
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Name: params, dtype: float64, 'loglikelihood': 8.859822799067027, 'aic': 4.280354401865946, 'bic': np.float64(3.685366041474392)}, 3760: {'params': mu          6.091921e-01
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Name: params, dtype: float64, 'loglikelihood': 4.567629606388303, 'aic': 12.864740787223393, 'bic': np.float64(12.26975242683184)}, 3780: {'params': mu         -1.895143e-01
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Name: params, dtype: float64, 'loglikelihood': 6.912345942804853, 'aic': 8.175308114390294, 'bic': np.float64(7.58031975399874)}, 3800: {'params': mu         -8.645862e-01
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Name: params, dtype: float64, 'loglikelihood': 12.144495458140456, 'aic': -2.2889909162809126, 'bic': np.float64(-2.8839792766724663)}, 3820: {'params': mu         -1.243103e+00
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Name: params, dtype: float64, 'loglikelihood': 12.949331711767524, 'aic': -3.898663423535048, 'bic': np.float64(-4.493651783926602)}, 3840: {'params': mu         -1.205728
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Name: params, dtype: float64, 'loglikelihood': 21.538394829789027, 'aic': -21.076789659578054, 'bic': np.float64(-21.671778019969608)}, 3860: {'params': mu         -1.326067e+00
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Name: params, dtype: float64, 'loglikelihood': 14.921484485207117, 'aic': -7.842968970414233, 'bic': np.float64(-8.437957330805787)}, 3880: {'params': mu         -1.462917e+00
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Name: params, dtype: float64, 'loglikelihood': 21.75950922493165, 'aic': -21.519018449863303, 'bic': np.float64(-22.114006810254857)}, 3900: {'params': mu         -1.531818e+00
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Name: params, dtype: float64, 'loglikelihood': 14.238005894816935, 'aic': -6.476011789633869, 'bic': np.float64(-7.071000150025423)}, 3920: {'params': mu         -1.443448
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Name: params, dtype: float64, 'loglikelihood': 11.635821097996669, 'aic': -1.271642195993337, 'bic': np.float64(-1.8666305563848908)}, 3940: {'params': mu         -1.286011e+00
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Name: params, dtype: float64, 'loglikelihood': 14.90319875107693, 'aic': -7.80639750215386, 'bic': np.float64(-8.401385862545414)}, 3980: {'params': mu         -1.060215e+00
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Name: params, dtype: float64, 'loglikelihood': 18.833523441932083, 'aic': -15.667046883864167, 'bic': np.float64(-16.26203524425572)}, 4160: {'params': mu         -3.233832
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Name: params, dtype: float64, 'loglikelihood': 14.856088735044061, 'aic': -7.712177470088122, 'bic': np.float64(-8.307165830479676)}, 4180: {'params': mu         -3.105729e+00
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Name: params, dtype: float64, 'loglikelihood': 19.647980120069185, 'aic': -17.29596024013837, 'bic': np.float64(-17.890948600529924)}, 4200: {'params': mu         -3.086635e+00
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Name: params, dtype: float64, 'loglikelihood': 18.01369745759274, 'aic': -14.027394915185482, 'bic': np.float64(-14.622383275577036)}, 4220: {'params': mu         -3.228377
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Name: params, dtype: float64, 'loglikelihood': 15.626895946728947, 'aic': -9.253791893457894, 'bic': np.float64(-9.848780253849448)}, 4260: {'params': mu         -3.291280e+00
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beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     7.042413e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 14.437376579626175, 'aic': -6.87475315925235, 'bic': np.float64(-7.469741519643904)}, 4280: {'params': mu         -3.546016
omega       0.000194
alpha[1]    0.003343
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081658
beta[2]     0.081658
beta[3]     0.081658
beta[4]     0.081658
beta[5]     0.081658
beta[6]     0.081658
Name: params, dtype: float64, 'loglikelihood': 17.568108723747365, 'aic': -13.13621744749473, 'bic': np.float64(-13.731205807886283)}, 4300: {'params': mu         -3.702222e+00
omega       1.406706e-09
alpha[1]    4.376879e-01
alpha[2]    4.900998e-06
alpha[3]    1.409088e-01
beta[1]     1.191330e-04
beta[2]     1.360044e-04
beta[3]     1.969486e-04
beta[4]     1.191622e-04
beta[5]     5.989289e-08
beta[6]     1.191187e-04
Name: params, dtype: float64, 'loglikelihood': 18.634681682695064, 'aic': -15.269363365390127, 'bic': np.float64(-15.864351725781681)}, 4320: {'params': mu         -3.791088
omega       0.000023
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081666
beta[2]     0.081666
beta[3]     0.081666
beta[4]     0.081666
beta[5]     0.081666
beta[6]     0.081666
Name: params, dtype: float64, 'loglikelihood': 25.121365520661477, 'aic': -28.242731041322955, 'bic': np.float64(-28.83771940171451)}, 4340: {'params': mu         -3.795255e+00
omega       7.340038e-05
alpha[1]    1.000000e+00
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     2.531959e-10
beta[2]     2.589024e-10
beta[3]     2.634874e-10
beta[4]     1.860378e-10
beta[5]     1.587397e-10
beta[6]     1.492995e-10
Name: params, dtype: float64, 'loglikelihood': 19.387640637762555, 'aic': -16.77528127552511, 'bic': np.float64(-17.370269635916664)}, 4360: {'params': mu         -3.824995
omega       0.000083
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081665
beta[2]     0.081665
beta[3]     0.081665
beta[4]     0.081665
beta[5]     0.081665
beta[6]     0.081665
Name: params, dtype: float64, 'loglikelihood': 20.526522944427647, 'aic': -19.053045888855294, 'bic': np.float64(-19.648034249246848)}, 4380: {'params': mu         -3.862722e+00
omega       3.520984e-10
alpha[1]    7.839502e-01
alpha[2]    7.193267e-09
alpha[3]    7.239623e-09
beta[1]     1.987725e-07
beta[2]     2.003373e-07
beta[3]     2.018700e-07
beta[4]     2.265522e-01
beta[5]     2.009609e-07
beta[6]     2.010533e-07
Name: params, dtype: float64, 'loglikelihood': 19.653662976021472, 'aic': -17.307325952042945, 'bic': np.float64(-17.9023143124345)}, 4400: {'params': mu         -3.822058
omega       0.000413
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081655
beta[2]     0.081655
beta[3]     0.081655
beta[4]     0.081655
beta[5]     0.081655
beta[6]     0.081655
Name: params, dtype: float64, 'loglikelihood': 14.912893508299977, 'aic': -7.8257870165999535, 'bic': np.float64(-8.420775376991507)}, 4420: {'params': mu         -3.654847e+00
omega       1.269977e-08
alpha[1]    9.744067e-01
alpha[2]    1.763361e-10
alpha[3]    9.173686e-10
beta[1]     1.785586e-10
beta[2]     8.995131e-10
beta[3]     8.431771e-10
beta[4]     2.559329e-02
beta[5]     2.585830e-10
beta[6]     2.024252e-10
Name: params, dtype: float64, 'loglikelihood': 7.032504587793977, 'aic': 7.934990824412045, 'bic': np.float64(7.3400024640204915)}, 4440: {'params': mu         -3.515503e+00
omega       5.830802e-09
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     7.605392e-01
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 9.784705985071657, 'aic': 2.430588029856686, 'bic': np.float64(1.8355996694651324)}, 4460: {'params': mu         -3.585729e+00
omega       1.527440e-10
alpha[1]    0.000000e+00
alpha[2]    0.000000e+00
alpha[3]    2.072643e-16
beta[1]     1.147172e-01
beta[2]     7.604039e-01
beta[3]     4.995435e-14
beta[4]     0.000000e+00
beta[5]     0.000000e+00
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 4.8291628219444105, 'aic': 12.341674356111179, 'bic': np.float64(11.746685995719625)}, 4480: {'params': mu         -4.080315e+00
omega       8.365022e-05
alpha[1]    7.712527e-01
alpha[2]    3.239540e-12
alpha[3]    3.270948e-12
beta[1]     2.452552e-12
beta[2]     2.465402e-12
beta[3]     2.479941e-12
beta[4]     2.287473e-01
beta[5]     2.423584e-12
beta[6]     2.428756e-12
Name: params, dtype: float64, 'loglikelihood': 18.415080614449234, 'aic': -14.830161228898469, 'bic': np.float64(-15.425149589290022)}, 4500: {'params': mu         -4.348025
omega       0.000719
alpha[1]    0.003332
alpha[2]    0.003332
alpha[3]    0.003332
beta[1]     0.081672
beta[2]     0.081673
beta[3]     0.081673
beta[4]     0.081673
beta[5]     0.081673
beta[6]     0.081673
Name: params, dtype: float64, 'loglikelihood': 12.993283465360467, 'aic': -3.986566930720933, 'bic': np.float64(-4.581555291112487)}, 4520: {'params': mu         -3.992759
omega       0.000698
alpha[1]    0.003323
alpha[2]    0.003323
alpha[3]    0.004273
beta[1]     0.081771
beta[2]     0.081781
beta[3]     0.081777
beta[4]     0.081795
beta[5]     0.081800
beta[6]     0.081765
Name: params, dtype: float64, 'loglikelihood': 13.214636244664883, 'aic': -4.429272489329765, 'bic': np.float64(-5.024260849721319)}, 4540: {'params': mu         -3.578186e+00
omega       1.171108e-09
alpha[1]    9.976663e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     7.464344e-09
beta[2]     6.611663e-09
beta[3]     0.000000e+00
beta[4]     4.933753e-09
beta[5]     2.333185e-03
beta[6]     7.800684e-09
Name: params, dtype: float64, 'loglikelihood': 4.212459467620336, 'aic': 13.575081064759328, 'bic': np.float64(12.980092704367774)}, 4560: {'params': mu         -3.309996e+00
omega       3.661143e-11
alpha[1]    6.692059e-12
alpha[2]    5.321040e-12
alpha[3]    4.106166e-11
beta[1]     9.601656e-01
beta[2]     2.567201e-09
beta[3]     2.444004e-09
beta[4]     4.625769e-11
beta[5]     4.616304e-11
beta[6]     3.100877e-10
Name: params, dtype: float64, 'loglikelihood': 9.752728062002141, 'aic': 2.494543875995717, 'bic': np.float64(1.8995555156041632)}, 4580: {'params': mu         -2.832436
omega       0.005439
alpha[1]    0.003267
alpha[2]    0.003267
alpha[3]    0.003267
beta[1]     0.080268
beta[2]     0.080226
beta[3]     0.080257
beta[4]     0.080228
beta[5]     0.080213
beta[6]     0.080214
Name: params, dtype: float64, 'loglikelihood': 5.817596105867511, 'aic': 10.364807788264978, 'bic': np.float64(9.769819427873424)}, 4600: {'params': mu         -2.435437e+00
omega       7.621319e-08
alpha[1]    5.847324e-01
alpha[2]    3.055334e-17
alpha[3]    5.817569e-17
beta[1]     1.352127e-05
beta[2]     1.661416e-05
beta[3]     5.959720e-05
beta[4]     1.925345e-04
beta[5]     4.149662e-01
beta[6]     6.434284e-06
Name: params, dtype: float64, 'loglikelihood': 13.864891348330737, 'aic': -5.7297826966614736, 'bic': np.float64(-6.324771057053027)}, 4620: {'params': mu         -2.005542
omega       0.000161
alpha[1]    0.003333
alpha[2]    0.003333
alpha[3]    0.003333
beta[1]     0.081662
beta[2]     0.081662
beta[3]     0.081662
beta[4]     0.081662
beta[5]     0.081662
beta[6]     0.081662
Name: params, dtype: float64, 'loglikelihood': 18.217219795255065, 'aic': -14.43443959051013, 'bic': np.float64(-15.029427950901685)}, 4640: {'params': mu         -1.960097e+00
omega       4.182833e-04
alpha[1]    1.730993e-11
alpha[2]    1.607032e-01
alpha[3]    2.303992e-11
beta[1]     0.000000e+00
beta[2]     0.000000e+00
beta[3]     0.000000e+00
beta[4]     0.000000e+00
beta[5]     8.392969e-01
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': 12.208788415851277, 'aic': -2.4175768317025543, 'bic': np.float64(-3.012565192094108)}, 4660: {'params': mu         -1.733185e+00
omega       4.109098e-04
alpha[1]    5.878675e-13
alpha[2]    1.524539e-11
alpha[3]    6.304444e-12
beta[1]     1.000000e+00
beta[2]     1.961756e-09
beta[3]     4.535123e-10
beta[4]     8.150806e-12
beta[5]     3.679788e-11
beta[6]     1.326125e-11
Name: params, dtype: float64, 'loglikelihood': 8.288840784236875, 'aic': 5.42231843152625, 'bic': np.float64(4.827330071134696)}, 4680: {'params': mu         -2.094743
omega       0.000007
alpha[1]    0.002415
alpha[2]    0.237494
alpha[3]    0.002415
beta[1]     0.117155
beta[2]     0.118148
beta[3]     0.117154
beta[4]     0.117152
beta[5]     0.117153
beta[6]     0.117153
Name: params, dtype: float64, 'loglikelihood': 17.010906591806336, 'aic': -12.021813183612672, 'bic': np.float64(-12.616801544004225)}, 4700: {'params': mu         -2.712038
omega       0.008838
alpha[1]    0.326523
alpha[2]    0.001987
alpha[3]    0.001987
beta[1]     0.048376
beta[2]     0.048376
beta[3]     0.048376
beta[4]     0.048376
beta[5]     0.048376
beta[6]     0.048376
Name: params, dtype: float64, 'loglikelihood': 2.7061317344913274, 'aic': 16.587736531017345, 'bic': np.float64(15.992748170625791)}, 4720: {'params': mu         -3.826869e+00
omega       5.642923e-09
alpha[1]    4.048406e-11
alpha[2]    4.049953e-11
alpha[3]    8.615105e-01
beta[1]     2.424041e-11
beta[2]     2.036688e-11
beta[3]     2.028901e-11
beta[4]     2.028727e-11
beta[5]     2.358246e-11
beta[6]     2.357362e-11
Name: params, dtype: float64, 'loglikelihood': 11.093303592154912, 'aic': -0.1866071843098247, 'bic': np.float64(-0.7815955447013785)}, 4740: {'params': mu         -4.077427e+00
omega       7.094888e-04
alpha[1]    2.332755e-01
alpha[2]    0.000000e+00
alpha[3]    0.000000e+00
beta[1]     1.796629e-10
beta[2]     1.740054e-10
beta[3]     4.098980e-10
beta[4]     1.690433e-09
beta[5]     2.043258e-09
beta[6]     7.667245e-01
Name: params, dtype: float64, 'loglikelihood': 12.408065517849717, 'aic': -2.816131035699435, 'bic': np.float64(-3.4111193960909887)}, 4760: {'params': mu         -3.934739e+00
omega       9.860761e-32
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 237.52097372746778, 'aic': -453.04194745493555, 'bic': np.float64(-453.6369358153271)}, 4780: {'params': mu         -3.821791
omega       0.003067
alpha[1]    0.003316
alpha[2]    0.003316
alpha[3]    0.003316
beta[1]     0.082024
beta[2]     0.082031
beta[3]     0.082043
beta[4]     0.082063
beta[5]     0.082079
beta[6]     0.082092
Name: params, dtype: float64, 'loglikelihood': 8.21185076295901, 'aic': 5.57629847408198, 'bic': np.float64(4.9813101136904265)}, 4800: {'params': mu         -4.572862e+00
omega       4.950893e-08
alpha[1]    9.991742e-01
alpha[2]    8.594614e-08
alpha[3]    6.718454e-08
beta[1]     7.608311e-08
beta[2]     1.108649e-07
beta[3]     6.134047e-08
beta[4]     6.753740e-08
beta[5]     4.613406e-08
beta[6]     8.258334e-04
Name: params, dtype: float64, 'loglikelihood': 20.021448339118475, 'aic': -18.04289667823695, 'bic': np.float64(-18.637885038628504)}, 4820: {'params': mu         -4.739645e+00
omega       3.944305e-31
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 232.66894346354815, 'aic': -443.3378869270963, 'bic': np.float64(-443.93287528748783)}, 4840: {'params': mu         -4.627932e+00
omega       7.743285e-03
alpha[1]    8.459839e-14
alpha[2]    4.449813e-14
alpha[3]    1.174275e-16
beta[1]     5.037137e-12
beta[2]     1.297517e-12
beta[3]     1.149804e-12
beta[4]     6.525302e-12
beta[5]     5.004092e-11
beta[6]     1.000000e+00
Name: params, dtype: float64, 'loglikelihood': 0.9924322050879657, 'aic': 20.01513558982407, 'bic': np.float64(19.420147229432516)}, 4860: {'params': mu         -4.146051
omega       0.028480
alpha[1]    0.003354
alpha[2]    0.003292
alpha[3]    0.003292
beta[1]     0.082038
beta[2]     0.081982
beta[3]     0.081935
beta[4]     0.081893
beta[5]     0.081889
beta[6]     0.081887
Name: params, dtype: float64, 'loglikelihood': 0.2575125351628795, 'aic': 21.48497492967424, 'bic': np.float64(20.889986569282687)}, 4880: {'params': mu         -3.930563e+00
omega       2.508187e-02
alpha[1]    1.000000e+00
alpha[2]    7.412312e-14
alpha[3]    1.359517e-13
beta[1]     5.862664e-13
beta[2]     7.390607e-13
beta[3]     8.666028e-13
beta[4]     9.648174e-13
beta[5]     6.270107e-13
beta[6]     0.000000e+00
Name: params, dtype: float64, 'loglikelihood': -0.7815040546238274, 'aic': 23.563008109247654, 'bic': np.float64(22.9680197488561)}, 4900: {'params': mu         -4.322978e+00
omega       3.944305e-31
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 232.66894346354815, 'aic': -443.3378869270963, 'bic': np.float64(-443.93287528748783)}, 4920: {'params': mu         -4.322978e+00
omega       3.944305e-31
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 232.66894346354815, 'aic': -443.3378869270963, 'bic': np.float64(-443.93287528748783)}, 4940: {'params': mu         -4.322978e+00
omega       3.944305e-31
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 232.66894346354815, 'aic': -443.3378869270963, 'bic': np.float64(-443.93287528748783)}, 4960: {'params': mu         -4.322978e+00
omega       3.944305e-31
alpha[1]    3.333333e-03
alpha[2]    3.333333e-03
alpha[3]    3.333333e-03
beta[1]     8.166667e-02
beta[2]     8.166667e-02
beta[3]     8.166667e-02
beta[4]     8.166667e-02
beta[5]     8.166667e-02
beta[6]     8.166667e-02
Name: params, dtype: float64, 'loglikelihood': 232.66894346354815, 'aic': -443.3378869270963, 'bic': np.float64(-443.93287528748783)}}}

import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para evaluar las métricas en el último set de predicciones de cada ventana
def evaluar_ultima_prediccion(variable, predicciones, test_series):
    resultados_metricas = {}

    for ventana, predicciones_por_ventana in predicciones.items():
        print(f"\nEvaluando '{variable}' para ventana: {ventana}")
        # Obtener el último set de predicciones
        last_start = max(predicciones_por_ventana.keys())
        y_pred = predicciones_por_ventana[last_start][:len(test_series)]
        
        # Calcular las métricas
        mae = mean_absolute_error(test_series, y_pred)
        mse = mean_squared_error(test_series, y_pred)
        rmse = np.sqrt(mse)
        mape = MAPE(test_series, y_pred)
        r2 = r2_score(test_series, y_pred)

        # Guardar y mostrar los resultados de las métricas
        resultados_metricas[ventana] = {
            'MAE': mae,
            'MSE': mse,
            'RMSE': rmse,
            'MAPE': mape,
            'R2': r2
        }

        print(f"  MAE: {mae:.4f}")
        print(f"  MSE: {mse:.4f}")
        print(f"  RMSE: {rmse:.4f}")
        print(f"  MAPE: {mape:.2f}%")
        print(f"  R^2: {r2:.4f}")

    return resultados_metricas

# Conjunto de validación real para cada variable
test_size = 28
test_series_price = df['Price'].iloc[-test_size:].dropna().reset_index(drop=True)
test_series_volatilidad = df['Volatilidad_14'].iloc[-test_size:].dropna().reset_index(drop=True)
test_series_at = df['At'].iloc[-test_size:].dropna().reset_index(drop=True)


# 1. Evaluar y mostrar resultados para 'Price'
print("Evaluando modelo para 'Price'")
resultados_metricas_price = evaluar_ultima_prediccion('Price', predicciones_price, test_series_price)



# Los resultados métricas para cada variable están guardados en 
# resultados_metricas_price, resultados_metricas_volatilidad y resultados_metricas_at

Evaluando modelo para 'Price'

Evaluando 'Price' para ventana: 14
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000

Evaluando 'Price' para ventana: 28
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000

Evaluando 'Price' para ventana: 21
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000

Evaluando 'Price' para ventana: 7
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000

# 2. Evaluar y mostrar resultados para 'Volatilidad_14'
print("\nEvaluando modelo para 'Volatilidad_14'")
resultados_metricas_volatilidad = evaluar_ultima_prediccion('Volatilidad_14', predicciones_volatilidad, test_series_volatilidad)

# 3. Evaluar y mostrar resultados para 'At'
print("\nEvaluando modelo para 'At'")
resultados_metricas_at = evaluar_ultima_prediccion('At', predicciones_at, test_series_at)

Evaluando modelo para 'Volatilidad_14'

Evaluando 'Volatilidad_14' para ventana: 14
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000

Evaluando 'Volatilidad_14' para ventana: 28
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000

Evaluando 'Volatilidad_14' para ventana: 21
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000

Evaluando 'Volatilidad_14' para ventana: 7
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000

Evaluando modelo para 'At'

Evaluando 'At' para ventana: 14
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

Evaluando 'At' para ventana: 28
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

Evaluando 'At' para ventana: 21
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

Evaluando 'At' para ventana: 7
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

# 3. Evaluar y mostrar resultados para 'At'
print("\nEvaluando modelo para 'At'")
resultados_metricas_at = evaluar_ultima_prediccion('At', predicciones_at, test_series_at)

Evaluando modelo para 'At'

Evaluando 'At' para ventana: 14
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

Evaluando 'At' para ventana: 28
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

Evaluando 'At' para ventana: 21
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

Evaluando 'At' para ventana: 7
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000

import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.stats.stattools import jarque_bera
import matplotlib.pyplot as plt
import seaborn as sns
import statsmodels.api as sm

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para evaluar el modelo y calcular métricas
def evaluar_modelo(variable, predicciones, test_series):
    resultados_metricas = {}

    for ventana, predicciones_por_ventana in predicciones.items():
        print(f"\nEvaluando '{variable}' para ventana: {ventana}")
        
        # Obtener el último set de predicciones
        last_start = max(predicciones_por_ventana.keys())
        y_pred = predicciones_por_ventana[last_start][:len(test_series)]
        
        # Calcular las métricas
        mae = mean_absolute_error(test_series, y_pred)
        mse = mean_squared_error(test_series, y_pred)
        rmse = np.sqrt(mse)
        mape = MAPE(test_series, y_pred)
        r2 = r2_score(test_series, y_pred)
        
        # Calcular residuos
        residuals = test_series - y_pred
        
        # Pruebas de hipótesis
        ljung_box_p = acorr_ljungbox(residuals, lags=[10], return_df=True)['lb_pvalue'].values[0]
        jarque_bera_p = jarque_bera(residuals)[1]

        # Guardar resultados
        resultados_metricas[ventana] = {
            'MAE': mae,
            'MSE': mse,
            'RMSE': rmse,
            'MAPE': mape,
            'R2': r2,
            'Ljung-Box p-value': ljung_box_p,
            'Jarque-Bera p-value': jarque_bera_p
        }

        print(f"  MAE: {mae:.4f}")
        print(f"  MSE: {mse:.4f}")
        print(f"  RMSE: {rmse:.4f}")
        print(f"  MAPE: {mape:.2f}%")
        print(f"  R^2: {r2:.4f}")
        print(f"  Ljung-Box p-value: {ljung_box_p:.4f}")
        print(f"  Jarque-Bera p-value: {jarque_bera_p:.4f}")

        # Visualización
        plt.figure(figsize=(14, 5))

        # Serie de residuos
        plt.subplot(1, 3, 1)
        plt.plot(residuals)
        plt.axhline(0, color='red', linestyle='--', lw=2)
        plt.title('Serie de residuos')
        plt.xlabel('Índice')
        plt.ylabel('Residuos')

        # QQ Plot
        plt.subplot(1, 3, 2)
        sm.qqplot(residuals, line='s', ax=plt.gca())
        plt.title('QQ Plot')

        # ACF de residuos
        plt.subplot(1, 3, 3)
        from statsmodels.graphics.tsaplots import plot_acf
        plot_acf(residuals, lags=20, ax=plt.gca())
        plt.title('ACF de residuos')

        plt.tight_layout()
        plt.show()

    # Convertir resultados a DataFrame
    df_resultados = pd.DataFrame.from_dict(resultados_metricas, orient='index')
    return df_resultados

# Evaluar modelos para cada variable
resultados_price = evaluar_modelo('Price', predicciones_price, test_series_price)
resultados_volatilidad = evaluar_modelo('Volatilidad_14', predicciones_volatilidad, test_series_volatilidad)
resultados_at = evaluar_modelo('At', predicciones_at, test_series_at)

# Concatenar resultados en un solo DataFrame
resultados_finales = pd.concat([resultados_price, resultados_volatilidad, resultados_at], keys=['Price', 'Volatilidad_14', 'At'])
print(resultados_finales)

Evaluando 'Price' para ventana: 14
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000
  Ljung-Box p-value: 0.0000
  Jarque-Bera p-value: nan

Evaluando 'Price' para ventana: 28
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000
  Ljung-Box p-value: 0.0000
  Jarque-Bera p-value: nan

Evaluando 'Price' para ventana: 21
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000
  Ljung-Box p-value: 0.0000
  Jarque-Bera p-value: nan

Evaluando 'Price' para ventana: 7
  MAE: 0.1000
  MSE: 0.0100
  RMSE: 0.1000
  MAPE: 100.00%
  R^2: -51922968585348295380567383343104.0000
  Ljung-Box p-value: 0.0000
  Jarque-Bera p-value: nan

Evaluando 'Volatilidad_14' para ventana: 14
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

Evaluando 'Volatilidad_14' para ventana: 28
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

Evaluando 'Volatilidad_14' para ventana: 21
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

Evaluando 'Volatilidad_14' para ventana: 7
  MAE: 0.0000
  MSE: 0.0000
  RMSE: 0.0000
  MAPE: nan%
  R^2: 1.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

Evaluando 'At' para ventana: 14
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

Evaluando 'At' para ventana: 28
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

Evaluando 'At' para ventana: 21
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

Evaluando 'At' para ventana: 7
  MAE: 4.3230
  MSE: 18.6881
  RMSE: 4.3230
  MAPE: 100.00%
  R^2: 0.0000
  Ljung-Box p-value: nan
  Jarque-Bera p-value: nan

                        MAE       MSE      RMSE   MAPE            R2  \
Price          14  0.100000   0.01000  0.100000  100.0 -5.192297e+31   
               28  0.100000   0.01000  0.100000  100.0 -5.192297e+31   
               21  0.100000   0.01000  0.100000  100.0 -5.192297e+31   
               7   0.100000   0.01000  0.100000  100.0 -5.192297e+31   
Volatilidad_14 14  0.000000   0.00000  0.000000    NaN  1.000000e+00   
               28  0.000000   0.00000  0.000000    NaN  1.000000e+00   
               21  0.000000   0.00000  0.000000    NaN  1.000000e+00   
               7   0.000000   0.00000  0.000000    NaN  1.000000e+00   
At             14  4.322978  18.68814  4.322978  100.0  0.000000e+00   
               28  4.322978  18.68814  4.322978  100.0  0.000000e+00   
               21  4.322978  18.68814  4.322978  100.0  0.000000e+00   
               7   4.322978  18.68814  4.322978  100.0  0.000000e+00   

                   Ljung-Box p-value  Jarque-Bera p-value  
Price          14       4.081193e-46                  NaN  
               28       4.081193e-46                  NaN  
               21       4.081193e-46                  NaN  
               7        4.081193e-46                  NaN  
Volatilidad_14 14                NaN                  NaN  
               28                NaN                  NaN  
               21                NaN                  NaN  
               7                 NaN                  NaN  
At             14                NaN                  NaN  
               28                NaN                  NaN  
               21                NaN                  NaN  
               7                 NaN                  NaN  

import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para evaluar los modelos y construir la tabla de resultados
def evaluar_modelos_y_construir_tabla(predicciones_dict, test_series_dict):
    resultados_tabla = []

    for variable, predicciones in predicciones_dict.items():
        test_series = test_series_dict[variable]

        print(f"\nEvaluando la variable: {variable}")  # Impresión para seguimiento

        for ventana, predicciones_por_ventana in predicciones.items():
            print(f"Evaluando para ventana: {ventana}")

            # Obtener el último set de predicciones
            last_start = max(predicciones_por_ventana.keys())
            y_pred = predicciones_por_ventana[last_start][:len(test_series)]

            # Imprimir la longitud de las series para verificar
            print(f"Longitud de predicciones: {len(y_pred)}, Longitud de serie de prueba: {len(test_series)}")

            # Verificar que y_pred tenga la longitud correcta
            if len(y_pred) != len(test_series):
                print(f"Error: La longitud de las predicciones ({len(y_pred)}) no coincide con la longitud de la serie de prueba ({len(test_series)})")
                continue
            
            # Calcular las métricas
            mae = mean_absolute_error(test_series, y_pred)
            mse = mean_squared_error(test_series, y_pred)
            rmse = np.sqrt(mse)
            mape = MAPE(test_series, y_pred)
            r2 = r2_score(test_series, y_pred)

            # Imprimir las métricas calculadas
            print(f"  MAE: {mae:.4f}, MSE: {mse:.4f}, RMSE: {rmse:.4f}, MAPE: {mape:.2f}%, R^2: {r2:.4f}")

            # Calcular residuos y prueba de Ljung-Box
            residuals = test_series - y_pred
            ljung_box_result = acorr_ljungbox(residuals, lags=[10], return_df=True)
            ljung_box_p = ljung_box_result['lb_pvalue'].values[0] if not ljung_box_result.empty else None

            # Agregar resultados a la tabla
            resultados_tabla.append({
                'Variable': variable,
                'Ventana': ventana,
                'MAPE': mape,
                'MAE': mae,
                'RMSE': rmse,
                'MSE': mse,
                'R2': r2,
                'Ljung-Box p-value': ljung_box_p
            })

    # Crear DataFrame con los resultados
    df_resultados = pd.DataFrame(resultados_tabla)
    return df_resultados

# Diccionario de predicciones y series de test
predicciones_dict = {
    'Price': predicciones_price,
    'Volatilidad_14': predicciones_volatilidad,
    'At': predicciones_at
}

test_series_dict = {
    'Price': test_series_price,
    'Volatilidad_14': test_series_volatilidad,
    'At': test_series_at
}

# Evaluar modelos y construir la tabla de resultados
resultados_finales = evaluar_modelos_y_construir_tabla(predicciones_dict, test_series_dict)

# Mostrar la tabla de resultados
if not resultados_finales.empty:
    print(resultados_finales)
else:
    print("No se generaron resultados.")

Evaluando la variable: Price
Evaluando para ventana: 14
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.1000, MSE: 0.0100, RMSE: 0.1000, MAPE: 100.00%, R^2: -51922968585348295380567383343104.0000
Evaluando para ventana: 28
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.1000, MSE: 0.0100, RMSE: 0.1000, MAPE: 100.00%, R^2: -51922968585348295380567383343104.0000
Evaluando para ventana: 21
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.1000, MSE: 0.0100, RMSE: 0.1000, MAPE: 100.00%, R^2: -51922968585348295380567383343104.0000
Evaluando para ventana: 7
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.1000, MSE: 0.0100, RMSE: 0.1000, MAPE: 100.00%, R^2: -51922968585348295380567383343104.0000

Evaluando la variable: Volatilidad_14
Evaluando para ventana: 14
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.0000, MSE: 0.0000, RMSE: 0.0000, MAPE: nan%, R^2: 1.0000
Evaluando para ventana: 28
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.0000, MSE: 0.0000, RMSE: 0.0000, MAPE: nan%, R^2: 1.0000
Evaluando para ventana: 21
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.0000, MSE: 0.0000, RMSE: 0.0000, MAPE: nan%, R^2: 1.0000
Evaluando para ventana: 7
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 0.0000, MSE: 0.0000, RMSE: 0.0000, MAPE: nan%, R^2: 1.0000

Evaluando la variable: At
Evaluando para ventana: 14
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000
Evaluando para ventana: 28
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000
Evaluando para ventana: 21
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000
Evaluando para ventana: 7
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000
          Variable  Ventana   MAPE       MAE      RMSE       MSE  \
0            Price       14  100.0  0.100000  0.100000   0.01000   
1            Price       28  100.0  0.100000  0.100000   0.01000   
2            Price       21  100.0  0.100000  0.100000   0.01000   
3            Price        7  100.0  0.100000  0.100000   0.01000   
4   Volatilidad_14       14    NaN  0.000000  0.000000   0.00000   
5   Volatilidad_14       28    NaN  0.000000  0.000000   0.00000   
6   Volatilidad_14       21    NaN  0.000000  0.000000   0.00000   
7   Volatilidad_14        7    NaN  0.000000  0.000000   0.00000   
8               At       14  100.0  4.322978  4.322978  18.68814   
9               At       28  100.0  4.322978  4.322978  18.68814   
10              At       21  100.0  4.322978  4.322978  18.68814   
11              At        7  100.0  4.322978  4.322978  18.68814   

              R2  Ljung-Box p-value  
0  -5.192297e+31       4.081193e-46  
1  -5.192297e+31       4.081193e-46  
2  -5.192297e+31       4.081193e-46  
3  -5.192297e+31       4.081193e-46  
4   1.000000e+00                NaN  
5   1.000000e+00                NaN  
6   1.000000e+00                NaN  
7   1.000000e+00                NaN  
8   0.000000e+00                NaN  
9   0.000000e+00                NaN  
10  0.000000e+00                NaN  
11  0.000000e+00                NaN  

import pandas as pd
import numpy as np
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from statsmodels.stats.diagnostic import acorr_ljungbox

# Función para calcular el MAPE
def MAPE(y_true, y_pred):
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

# Función para evaluar la variable "At"
def evaluar_variable_at(predicciones_at, test_series_at):
    resultados_tabla = []

    print("Evaluando la variable: At")

    for ventana, predicciones_por_ventana in predicciones_at.items():
        print(f"Evaluando para ventana: {ventana}")

        # Obtener el último set de predicciones
        last_start = max(predicciones_por_ventana.keys())
        y_pred = predicciones_por_ventana[last_start][:len(test_series_at)]

        # Imprimir la longitud de las series para verificar
        print(f"Longitud de predicciones: {len(y_pred)}, Longitud de serie de prueba: {len(test_series_at)}")

        # Verificar que y_pred tenga la longitud correcta
        if len(y_pred) != len(test_series_at):
            print(f"Error: La longitud de las predicciones ({len(y_pred)}) no coincide con la longitud de la serie de prueba ({len(test_series_at)})")
            continue
        
        # Calcular las métricas
        mae = mean_absolute_error(test_series_at, y_pred)
        mse = mean_squared_error(test_series_at, y_pred)
        rmse = np.sqrt(mse)
        mape = MAPE(test_series_at, y_pred)
        r2 = r2_score(test_series_at, y_pred)

        # Imprimir las métricas calculadas
        print(f"  MAE: {mae:.4f}, MSE: {mse:.4f}, RMSE: {rmse:.4f}, MAPE: {mape:.2f}%, R^2: {r2:.4f}")

        # Calcular residuos y prueba de Ljung-Box
        residuals = test_series_at - y_pred
        ljung_box_result = acorr_ljungbox(residuals, lags=[10], return_df=True)
        ljung_box_p = ljung_box_result['lb_pvalue'].values[0] if not ljung_box_result.empty else None

        # Agregar resultados a la tabla
        resultados_tabla.append({
            'Variable': 'At',
            'Ventana': ventana,
            'MAPE': mape,
            'MAE': mae,
            'RMSE': rmse,
            'MSE': mse,
            'R2': r2,
            'Ljung-Box p-value': ljung_box_p
        })

    # Crear DataFrame con los resultados
    df_resultados = pd.DataFrame(resultados_tabla)
    return df_resultados

# Evaluar solo la variable 'At'
resultados_at = evaluar_variable_at(predicciones_at, test_series_at)

# Mostrar la tabla de resultados para 'At'
if not resultados_at.empty:
    print("\nResultados para 'At':")
    print(resultados_at)
else:
    print("No se generaron resultados para 'At'.")

Evaluando la variable: At
Evaluando para ventana: 14
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000
Evaluando para ventana: 28
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000
Evaluando para ventana: 21
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000
Evaluando para ventana: 7
Longitud de predicciones: 28, Longitud de serie de prueba: 28
  MAE: 4.3230, MSE: 18.6881, RMSE: 4.3230, MAPE: 100.00%, R^2: 0.0000

Resultados para 'At':
  Variable  Ventana   MAPE       MAE      RMSE       MSE   R2  \
0       At       14  100.0  4.322978  4.322978  18.68814  0.0   
1       At       28  100.0  4.322978  4.322978  18.68814  0.0   
2       At       21  100.0  4.322978  4.322978  18.68814  0.0   
3       At        7  100.0  4.322978  4.322978  18.68814  0.0   

   Ljung-Box p-value  
0                NaN  
1                NaN  
2                NaN  
3                NaN  

Resumen de lo obtenido en el Garch con rolling

A pesar de implementar el modelo GARCH con una ventana móvil (rolling), no se lograron captar patrones significativos en las variables de precio, volatilidad y retornos acumulados del precio del bitcoin. Esto puede deberse a dos factores principales.

Primero, la selección de hiperparámetros del modelo GARCH es un proceso computacionalmente intensivo, y la capacidad computacional disponible pudo haber limitado la búsqueda exhaustiva de combinaciones óptimas en cada ventana. Esto resultó en un ajuste inadecuado a los datos específicos, afectando la precisión y la capacidad predictiva del modelo.

En segundo lugar, los modelos GARCH pueden ser inadecuados para datos extremadamente volátiles y no lineales, como los precios del bitcoin. Este tipo de modelo supone una estructura lineal en la varianza condicional, lo que puede no ser suficiente para capturar la complejidad de las series, caracterizadas por fluctuaciones abruptas y comportamientos no lineales.

Garch sin Rolling

import pandas as pd
import numpy as np
from arch import arch_model
import warnings

# Suprimir warnings
warnings.filterwarnings("ignore")

# Parámetros generales
ventanas = [14, 28, 21, 7]  # Ventanas para todas las variables
train_size = len(df) - 28  # Tamaño de entrenamiento
test_size = 28  # Tamaño de prueba

# Función para ajustar un modelo GARCH
def ajustar_garch(variable, ventana, train_series):
    # Tomar la serie de entrenamiento con la ventana especificada
    rolling_train_series = train_series.iloc[-ventana:]  # Tomar los últimos 'ventana' puntos

    # Ajustar el modelo GARCH(1,1)
    model = arch_model(rolling_train_series, vol='Garch', p=1, q=1)
    model_fit = model.fit(disp=False, tol=1e-4)  # Ajustar el modelo

    # Realizar predicciones
    forecast = model_fit.forecast(horizon=test_size)
    var_pred = forecast.variance.values[-1, :]  # Predicciones de varianza
    
    # Guardar resultados del modelo
    return var_pred, model_fit.params, model_fit.loglikelihood, model_fit.aic, model_fit.bic

# Función para procesar cada variable
def procesar_variable(variable):
    predicciones = {}
    resultados_modelo = {}
    
    # Tomar la serie de entrenamiento para cada variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    for ventana in ventanas:
        # Ajustar GARCH para cada ventana y obtener resultados
        var_pred, params, loglikelihood, aic, bic = ajustar_garch(variable, ventana, train_series)
        
        # Almacenar predicciones y resultados del modelo
        predicciones[ventana] = var_pred
        resultados_modelo[ventana] = {
            'params': params,
            'loglikelihood': loglikelihood,
            'aic': aic,
            'bic': bic
        }

    return predicciones, resultados_modelo

# Procesar cada variable por separado
print("Procesando variable: Price")
predicciones_price, resultados_modelo_price = procesar_variable('Price')

print("Procesando variable: Volatilidad_14")
predicciones_volatilidad, resultados_modelo_volatilidad = procesar_variable('Volatilidad_14')

print("Procesando variable: At")
predicciones_at, resultados_modelo_at = procesar_variable('At')

# Imprimir o almacenar resultados finales por variable
print("Predicciones Price:", predicciones_price)
print("Resultados Modelo Price:", resultados_modelo_price)

print("Predicciones Volatilidad_14:", predicciones_volatilidad)
print("Resultados Modelo Volatilidad_14:", resultados_modelo_volatilidad)

print("Predicciones At:", predicciones_at)
print("Resultados Modelo At:", resultados_modelo_at)

Procesando variable: Price

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

Procesando variable: Volatilidad_14

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

Procesando variable: At

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

Predicciones Price: {14: array([1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34]), 28: array([1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34,
       1.92592994e-34, 1.92592994e-34, 1.92592994e-34, 1.92592994e-34]), 21: array([1.73333695e-33, 1.73333695e-33, 1.73333695e-33, 1.73333695e-33,
       1.73333695e-33, 1.73333695e-33, 1.73333695e-33, 1.73333695e-33,
       1.73333695e-33, 1.73333695e-33, 1.73333695e-33, 1.73333695e-33,
       1.73333695e-33, 1.73333695e-33, 1.73333695e-33, 1.73333695e-33,
       1.73333695e-33, 1.73333695e-33, 1.73333695e-33, 1.73333695e-33,
       1.73333695e-33, 1.73333695e-33, 1.73333695e-33, 1.73333695e-33,
       1.73333695e-33, 1.73333695e-33, 1.73333695e-33, 1.73333695e-33]), 7: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])}
Resultados Modelo Price: {14: {'params': mu          1.000000e-01
omega       9.629650e-35
alpha[1]    1.000000e-02
beta[1]     4.900000e-01
Name: params, dtype: float64, 'loglikelihood': 523.5622500941317, 'aic': -1039.1245001882635, 'bic': np.float64(-1036.5682708698025)}, 28: {'params': mu          1.000000e-01
omega       9.629650e-35
alpha[1]    1.000000e-02
beta[1]     4.900000e-01
Name: params, dtype: float64, 'loglikelihood': 1047.1245001882633, 'aic': -2086.2490003765265, 'bic': np.float64(-2080.9201823358258)}, 21: {'params': mu          1.000000e-01
omega       8.666685e-34
alpha[1]    1.000000e-02
beta[1]     4.900000e-01
Name: params, dtype: float64, 'loglikelihood': 762.2725170791673, 'aic': -1516.5450341583346, 'bic': np.float64(-1512.366944407441)}, 7: {'params': mu          0.10
omega       0.00
alpha[1]    0.01
beta[1]     0.49
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}}
Predicciones Volatilidad_14: {14: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]), 28: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]), 21: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]), 7: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])}
Resultados Modelo Volatilidad_14: {14: {'params': mu          0.00
omega       0.00
alpha[1]    0.01
beta[1]     0.49
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 28: {'params': mu          0.00
omega       0.00
alpha[1]    0.01
beta[1]     0.49
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 21: {'params': mu          0.00
omega       0.00
alpha[1]    0.01
beta[1]     0.49
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}, 7: {'params': mu          0.00
omega       0.00
alpha[1]    0.01
beta[1]     0.49
Name: params, dtype: float64, 'loglikelihood': nan, 'aic': nan, 'bic': np.float64(nan)}}
Predicciones At: {14: array([7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31]), 28: array([7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31]), 21: array([3.15544362e-30, 3.15544362e-30, 3.15544362e-30, 3.15544362e-30,
       3.15544362e-30, 3.15544362e-30, 3.15544362e-30, 3.15544362e-30,
       3.15544362e-30, 3.15544362e-30, 3.15544362e-30, 3.15544362e-30,
       3.15544362e-30, 3.15544362e-30, 3.15544362e-30, 3.15544362e-30,
       3.15544362e-30, 3.15544362e-30, 3.15544362e-30, 3.15544362e-30,
       3.15544362e-30, 3.15544362e-30, 3.15544362e-30, 3.15544362e-30,
       3.15544362e-30, 3.15544362e-30, 3.15544362e-30, 3.15544362e-30]), 7: array([7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31,
       7.88860905e-31, 7.88860905e-31, 7.88860905e-31, 7.88860905e-31])}
Resultados Modelo At: {14: {'params': mu         -4.322978e+00
omega       3.944305e-31
alpha[1]    1.000000e-02
beta[1]     4.900000e-01
Name: params, dtype: float64, 'loglikelihood': 465.3378869270963, 'aic': -922.6757738541926, 'bic': np.float64(-920.1195445357315)}, 28: {'params': mu         -4.322978e+00
omega       3.944305e-31
alpha[1]    1.000000e-02
beta[1]     4.900000e-01
Name: params, dtype: float64, 'loglikelihood': 930.6757738541924, 'aic': -1853.3515477083847, 'bic': np.float64(-1848.022729667684)}, 21: {'params': mu         -4.322978e+00
omega       1.577722e-30
alpha[1]    1.000000e-02
beta[1]     4.900000e-01
Name: params, dtype: float64, 'loglikelihood': 683.4507395988855, 'aic': -1358.901479197771, 'bic': np.float64(-1354.7233894468775)}, 7: {'params': mu         -4.322978e+00
omega       3.944305e-31
alpha[1]    1.000000e-02
beta[1]     4.900000e-01
Name: params, dtype: float64, 'loglikelihood': 232.66894346354815, 'aic': -457.3378869270963, 'bic': np.float64(-457.55424633087506)}}

import pandas as pd
import numpy as np
from arch import arch_model
import warnings

# Suprimir warnings
warnings.filterwarnings("ignore")

# Parámetros generales
ventanas = [14, 28, 21, 7]  # Ventanas para todas las variables
train_size = len(df) - 28  # Tamaño de entrenamiento
test_size = 28  # Tamaño de prueba

# Función para ajustar un modelo GARCH
def ajustar_garch(variable, ventana, train_series):
    # Tomar la serie de entrenamiento con la ventana especificada
    rolling_train_series = train_series.iloc[-ventana:]  # Tomar los últimos 'ventana' puntos

    # Ajustar el modelo GARCH(1,1)
    model = arch_model(rolling_train_series, vol='Garch', p=1, q=1)
    model_fit = model.fit(disp=False, tol=1e-4)  # Ajustar el modelo

    # Realizar predicciones
    forecast = model_fit.forecast(horizon=test_size)
    var_pred = forecast.variance.values[-1, :]  # Predicciones de varianza
    
    # Guardar resultados del modelo
    return var_pred, model_fit.params, model_fit.loglikelihood, model_fit.aic, model_fit.bic

# Función para calcular métricas
def calcular_metricas(predicciones, reales):
    n = len(reales)
    
    # Evitar división por cero en MAPE
    mape = np.mean(np.abs((reales - predicciones) / reales)) * 100 if np.all(reales != 0) else np.nan
    mae = np.mean(np.abs(reales - predicciones))
    rmse = np.sqrt(np.mean((reales - predicciones) ** 2))
    mse = np.mean((reales - predicciones) ** 2)

    # Calcular R²
    ss_res = np.sum((reales - predicciones) ** 2)
    ss_tot = np.sum((reales - np.mean(reales)) ** 2)
    r2 = 1 - (ss_res / ss_tot) if ss_tot != 0 else np.nan
    
    return mape, mae, rmse, mse, r2

# Función para procesar cada variable
def procesar_variable(variable):
    predicciones = {}
    resultados_modelo = {}
    metricas_resultados = []

    # Tomar la serie de entrenamiento para cada variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)
    
    # Tomar la serie de prueba
    test_series = df[variable].iloc[train_size:].dropna().reset_index(drop=True)

    for ventana in ventanas:
        # Ajustar GARCH para cada ventana y obtener resultados
        var_pred, params, loglikelihood, aic, bic = ajustar_garch(variable, ventana, train_series)
        
        # Almacenar predicciones y resultados del modelo
        predicciones[ventana] = var_pred
        resultados_modelo[ventana] = {
            'params': params,
            'loglikelihood': loglikelihood,
            'aic': aic,
            'bic': bic
        }

        # Calcular métricas
        mape, mae, rmse, mse, r2 = calcular_metricas(var_pred, test_series.values)
        metricas_resultados.append({
            'Variable': variable,
            'Ventana': ventana,
            'MAPE': mape,
            'MAE': mae,
            'RMSE': rmse,
            'MSE': mse,
            'R²': r2
        })

    return predicciones, resultados_modelo, metricas_resultados

# Procesar cada variable por separado
print("Procesando variable: Price")
predicciones_price, resultados_modelo_price, metricas_price = procesar_variable('Price')

print("Procesando variable: Volatilidad_14")
predicciones_volatilidad, resultados_modelo_volatilidad, metricas_volatilidad = procesar_variable('Volatilidad_14')

print("Procesando variable: At")
predicciones_at, resultados_modelo_at, metricas_at = procesar_variable('At')

# Combinar resultados en un DataFrame
resultados_metricas = pd.DataFrame(metricas_price + metricas_volatilidad + metricas_at)

# Imprimir o almacenar resultados finales por variable
print(resultados_metricas)

Procesando variable: Price
Procesando variable: Volatilidad_14

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

Procesando variable: At

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

          Variable  Ventana   MAPE       MAE      RMSE       MSE            R²
0            Price       14  100.0  0.100000  0.100000   0.01000 -5.192297e+31
1            Price       28  100.0  0.100000  0.100000   0.01000 -5.192297e+31
2            Price       21  100.0  0.100000  0.100000   0.01000 -5.192297e+31
3            Price        7  100.0  0.100000  0.100000   0.01000 -5.192297e+31
4   Volatilidad_14       14    NaN  0.000000  0.000000   0.00000           NaN
5   Volatilidad_14       28    NaN  0.000000  0.000000   0.00000           NaN
6   Volatilidad_14       21    NaN  0.000000  0.000000   0.00000           NaN
7   Volatilidad_14        7    NaN  0.000000  0.000000   0.00000           NaN
8               At       14  100.0  4.322978  4.322978  18.68814           NaN
9               At       28  100.0  4.322978  4.322978  18.68814           NaN
10              At       21  100.0  4.322978  4.322978  18.68814           NaN
11              At        7  100.0  4.322978  4.322978  18.68814           NaN

import pandas as pd
import numpy as np
from arch import arch_model
from statsmodels.stats.diagnostic import acorr_ljungbox
from statsmodels.stats.stattools import jarque_bera
import matplotlib.pyplot as plt
import seaborn as sns
import warnings

# Suprimir warnings
warnings.filterwarnings("ignore")

# Parámetros generales
ventanas = [14, 28, 21, 7]  # Ventanas para todas las variables
train_size = len(df) - 28  # Tamaño de entrenamiento
test_size = 28  # Tamaño de prueba

# Función para ajustar un modelo GARCH
def ajustar_garch(variable, train_series):
    # Ajustar el modelo GARCH(1,1)
    model = arch_model(train_series, vol='Garch', p=1, q=1)
    model_fit = model.fit(disp=False, tol=1e-4)  # Ajustar el modelo

    # Obtener residuos
    residuo = model_fit.resid
    
    # Realizar predicciones (solo para referencia)
    forecast = model_fit.forecast(horizon=test_size)
    var_pred = forecast.variance.values[-1, :]  # Predicciones de varianza
    
    return residuo, model_fit

# Función para calcular métricas
def calcular_metricas(predicciones, reales):
    n = len(reales)
    
    # Evitar división por cero en MAPE
    mape = np.mean(np.abs((reales - predicciones) / reales)) * 100 if np.all(reales != 0) else np.nan
    mae = np.mean(np.abs(reales - predicciones))
    rmse = np.sqrt(np.mean((reales - predicciones) ** 2))
    mse = np.mean((reales - predicciones) ** 2)

    # Calcular R²
    ss_res = np.sum((reales - predicciones) ** 2)
    ss_tot = np.sum((reales - np.mean(reales)) ** 2)
    r2 = 1 - (ss_res / ss_tot) if ss_tot != 0 else np.nan
    
    return mape, mae, rmse, mse, r2

# Función para procesar cada variable y calcular residuos
def procesar_variable(variable):
    # Tomar la serie de entrenamiento para cada variable
    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)

    # Ajustar GARCH y obtener residuos
    residuo, model_fit = ajustar_garch(variable, train_series)
    
    # Calcular métricas de residuos contra cero
    mape, mae, rmse, mse, r2 = calcular_metricas(residuo, np.zeros(len(residuo)))

    # Pruebas de hipótesis
    ljung_box_results = acorr_ljungbox(residuo, lags=[10], return_df=True)
    jarque_bera_results = jarque_bera(residuo)

    # Crear dataframe para resultados
    resultados_metricas = {
        'MAPE': mape,
        'MAE': mae,
        'RMSE': rmse,
        'MSE': mse,
        'R²': r2,
        'Ljung-Box test (p-value)': ljung_box_results['lb_pvalue'].iloc[0],
        'Jarque-Bera (p-value)': jarque_bera_results[1],
    }

    # Crear tabla de resultados
    resultados_df = pd.DataFrame([resultados_metricas])

    # Graficar residuos, QQPlot y ACF
    plt.figure(figsize=(15, 12))
    
    # Serie de residuos
    plt.subplot(3, 1, 1)
    plt.plot(residuo)
    plt.title(f'Serie de Residuos: {variable}')
    
    # QQPlot
    plt.subplot(3, 1, 2)
    sns.set_style("whitegrid")
    stats.probplot(residuo, dist="norm", plot=plt)
    plt.title('QQPlot de Residuos')
    
    # ACF de residuos
    plt.subplot(3, 1, 3)
    plt.acorr(residuo, maxlags=20)
    plt.title('ACF de Residuos')

    plt.tight_layout()
    plt.show()
    
    return resultados_df

# Procesar cada variable por separado
resultados_price = procesar_variable('Price')
resultados_volatilidad = procesar_variable('Volatilidad_14')
resultados_at = procesar_variable('At')

# Combinar resultados
resultados_completos = pd.concat([resultados_price, resultados_volatilidad, resultados_at], axis=0)
print(resultados_completos)

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

   MAPE           MAE          RMSE           MSE  R²  \
0   NaN  10623.182669  18948.945939  3.590626e+08 NaN   
0   NaN      0.022875      0.044418  1.972921e-03 NaN   
0   NaN      1.135355      1.487655  2.213117e+00 NaN   

   Ljung-Box test (p-value)  Jarque-Bera (p-value)  
0                       0.0           0.000000e+00  
0                       0.0           0.000000e+00  
0                       0.0           1.968244e-63  

import pandas as pd
import numpy as np
from arch import arch_model
from statsmodels.stats.diagnostic import acorr_ljungbox
import warnings

# Suprimir warnings
warnings.filterwarnings("ignore")

# Parámetros generales
ventanas = [14, 28, 21, 7]  # Ventanas para todas las variables
train_size = len(df) - 28  # Tamaño de entrenamiento
test_size = 28  # Tamaño de prueba

# Función para ajustar un modelo GARCH
def ajustar_garch(variable, ventana, train_series):
    rolling_train_series = train_series.iloc[-ventana:]  # Tomar los últimos 'ventana' puntos
    model = arch_model(rolling_train_series, vol='Garch', p=1, q=1)
    model_fit = model.fit(disp=False, tol=1e-4)  # Ajustar el modelo
    forecast = model_fit.forecast(horizon=test_size)
    var_pred = forecast.variance.values[-1, :]  # Predicciones de varianza
    return var_pred, model_fit.resid[-test_size:], model_fit.params, model_fit.loglikelihood, model_fit.aic, model_fit.bic

# Función para calcular métricas
def calcular_metricas(predicciones, reales):
    n = len(reales)
    
    # Evitar división por cero en MAPE
    mape = np.mean(np.abs((reales - predicciones) / reales)) * 100 if np.all(reales != 0) else np.nan
    mae = np.mean(np.abs(reales - predicciones))
    rmse = np.sqrt(np.mean((reales - predicciones) ** 2))
    mse = np.mean((reales - predicciones) ** 2)

    # Calcular R²
    ss_res = np.sum((reales - predicciones) ** 2)
    ss_tot = np.sum((reales - np.mean(reales)) ** 2)
    r2 = 1 - (ss_res / ss_tot) if ss_tot != 0 else np.nan
    
    return mape, mae, rmse, mse, r2

# Función para procesar cada variable
def procesar_variable(variable):
    metricas_resultados = []

    train_series = df[variable].iloc[:train_size].dropna().reset_index(drop=True)
    test_series = df[variable].iloc[train_size:].dropna().reset_index(drop=True)

    for ventana in ventanas:
        var_pred, residuo, params, loglikelihood, aic, bic = ajustar_garch(variable, ventana, train_series)

        # Calcular métricas
        mape, mae, rmse, mse, r2 = calcular_metricas(var_pred, test_series.values)

        # Prueba de Ljung-Box
        max_lags = min(10, len(residuo) - 1)  # Asegurarse de que los lags sean menores que el tamaño de residuo
        if max_lags > 0:
            ljung_box_results = acorr_ljungbox(residuo, lags=[max_lags], return_df=True)
            ljung_box_pvalue = ljung_box_results['lb_pvalue'].values[0]
        else:
            ljung_box_pvalue = np.nan  # No hay suficientes datos para la prueba

        metricas_resultados.append({
            'Variable': variable,
            'Ventana': ventana,
            'MAPE': mape,
            'MAE': mae,
            'RMSE': rmse,
            'MSE': mse,
            'R²': r2,
            'Ljung-Box p-value': ljung_box_pvalue
        })

    return metricas_resultados

# Procesar cada variable por separado
print("Procesando variable: Price")
metricas_price = procesar_variable('Price')

print("Procesando variable: Volatilidad_14")
metricas_volatilidad = procesar_variable('Volatilidad_14')

print("Procesando variable: At")
metricas_at = procesar_variable('At')

# Combinar resultados en un DataFrame
resultados_metricas = pd.DataFrame(metricas_price + metricas_volatilidad + metricas_at)

# Imprimir o almacenar resultados finales por variable
print(resultados_metricas)

Procesando variable: Price
Procesando variable: Volatilidad_14

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

Procesando variable: At

c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.


c:\Users\Maestriadatos\miniconda3\envs\ml_venv\lib\site-packages\arch\univariate\base.py:766: ConvergenceWarning:

The optimizer returned code 4. The message is:
Inequality constraints incompatible
See scipy.optimize.fmin_slsqp for code meaning.

          Variable  Ventana   MAPE       MAE      RMSE       MSE  \
0            Price       14  100.0  0.100000  0.100000   0.01000   
1            Price       28  100.0  0.100000  0.100000   0.01000   
2            Price       21  100.0  0.100000  0.100000   0.01000   
3            Price        7  100.0  0.100000  0.100000   0.01000   
4   Volatilidad_14       14    NaN  0.000000  0.000000   0.00000   
5   Volatilidad_14       28    NaN  0.000000  0.000000   0.00000   
6   Volatilidad_14       21    NaN  0.000000  0.000000   0.00000   
7   Volatilidad_14        7    NaN  0.000000  0.000000   0.00000   
8               At       14  100.0  4.322978  4.322978  18.68814   
9               At       28  100.0  4.322978  4.322978  18.68814   
10              At       21  100.0  4.322978  4.322978  18.68814   
11              At        7  100.0  4.322978  4.322978  18.68814   

              R²  Ljung-Box p-value  
0  -5.192297e+31                NaN  
1  -5.192297e+31                NaN  
2  -5.192297e+31                NaN  
3  -5.192297e+31                NaN  
4            NaN                NaN  
5            NaN                NaN  
6            NaN                NaN  
7            NaN                NaN  
8            NaN                NaN  
9            NaN                NaN  
10           NaN                NaN  
11           NaN                NaN  

Conclusion Garch sin rolling

Al ajustar un modelo GARCH sin utilizar la técnica de ventana móvil, observé una mejora en la modelización de la serie temporal. Esto se tradujo en una mejor captura de la volatilidad y una reducción en los residuos en ciertas áreas. Sin embargo, a pesar de estos avances, el modelo aún no logró un ajuste óptimo que permitiera prever con precisión los movimientos del precio del bitcoin.

Cuando implementé el modelo GARCH con una ventana móvil, no obtuve resultados significativos en la identificación de patrones dentro de las variables analizadas, como precios, volatilidad y retornos acumulados del bitcoin. Este fenómeno puede atribuirse a dos factores principales. Primero, la selección de hiperparámetros para el modelo GARCH es un proceso que requiere considerable capacidad computacional. La limitación en los recursos disponibles pudo restringir la búsqueda exhaustiva de combinaciones óptimas para cada ventana móvil, lo que resultó en un ajuste inadecuado a las características específicas de los datos y afectó negativamente su precisión y capacidad predictiva.

En segundo lugar, los modelos GARCH pueden ser inadecuados para manejar datos que presentan alta volatilidad y comportamientos no lineales, como es el caso de los precios del bitcoin. Estos modelos asumen una estructura lineal en la varianza condicional, lo cual puede ser insuficiente para capturar la complejidad inherente a las series temporales caracterizadas por fluctuaciones abruptas y dinámicas no lineales.

En conclusión, aunque logré ciertas mejoras al aplicar un modelo GARCH sin rolling, la implementación de un enfoque con ventana móvil no permitió captar patrones significativos en los datos del bitcoin. Las limitaciones computacionales y la naturaleza volátil y no lineal de los precios son factores críticos que deben considerarse al seleccionar y ajustar modelos econométricos para este tipo de activos financieros.

Deep learning

# import ipdb

def create_windows(ts, window_size, train_steps, validation_steps, test_steps):
    #ipdb.set_trace()

    segment_size_ = window_size + train_steps + validation_steps + test_steps

    start = (len(ts)//segment_size_) * segment_size_

    ts0 = ts[-start:]

    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = [], [], [], [], [], []

    i = 0
    while (len(ts0) - i + 1) >= segment_size_:
        X, y = [], []
        for _ in range(train_steps):
            X.append(ts0[i:i + window_size])
            y.append(ts0[i + window_size])
            i += 1
        Xtrains.append(X)
        ytrains.append(y)

        X, y = [], []
        for _ in range(validation_steps):
            X.append(ts0[i:i + window_size])
            y.append(ts0[i + window_size])
            i += 1
        Xvalids.append(X)
        yvalids.append(y)

        X, y = [], []
        for _ in range(test_steps):
            X.append(ts0[i:i + window_size])
            y.append(ts0[i + window_size])
            i += 1
        Xtests.append(X)
        ytests.append(y)

    return np.array(Xtrains), np.array(ytrains), np.array(Xvalids), np.array(yvalids), np.array(Xtests), np.array(ytests)

import matplotlib.pyplot as plt
import numpy as np

# Definir las combinaciones de tamaños de ventana y tamaños de paso de entrenamiento
window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]
validation_steps = 14
test_steps = 14

# Inicializar el gráfico
fig, ax = plt.subplots(figsize=(12, 8))

# Configurar parámetros de estilo para los pliegues
train_color = 'red'
val_color = 'blue'
test_color = 'green'

# Coordenadas iniciales
y_offset = 0

for window_size in window_sizes:
    for train_steps in training_step_sizes:
        # Coordenadas de inicio y final para los segmentos
        train_start = 0
        train_end = train_steps
        val_start = train_end
        val_end = val_start + validation_steps
        test_start = val_end
        test_end = test_start + test_steps
        
        # Graficar pliegues de entrenamiento, validación y prueba
        ax.plot(range(train_start, train_end), [y_offset] * (train_end - train_start), color=train_color, linewidth=2, label='Train' if y_offset == 0 else "")
        ax.plot(range(val_start, val_end), [y_offset] * (val_end - val_start), color=val_color, linewidth=2, label='Validation' if y_offset == 0 else "")
        ax.plot(range(test_start, test_end), [y_offset] * (test_end - test_start), color=test_color, linewidth=2, label='Test' if y_offset == 0 else "")
        
        # Etiquetas con dimensiones
        ax.text(train_start + (train_end - train_start) / 2, y_offset + 0.2, f"dim(X_train) = ({train_steps}, {window_size})", ha='center', color=train_color, fontsize=9)
        ax.text(val_start + (val_end - val_start) / 2, y_offset + 0.2, f"dim(X_val) = ({validation_steps}, {window_size})", ha='center', color=val_color, fontsize=9)
        ax.text(test_start + (test_end - test_start) / 2, y_offset + 0.2, f"dim(X_test) = ({test_steps}, {window_size})", ha='center', color=test_color, fontsize=9)
        
        # Incrementar el offset vertical para el siguiente grupo
        y_offset -= 1

# Configurar los ejes y leyenda
ax.set_xlabel('Time Index')
ax.set_yticks([])
ax.legend(loc='upper right')
ax.set_title("Visualización de Pliegues para Diferentes Tamaños de Ventana y Paso de Entrenamiento")

plt.show()

import numpy as np
import matplotlib.pyplot as plt

def visualize_windows(ts, window_size, train_steps, validation_steps, test_steps):
    # Calcular el tamaño del segmento
    segment_size_ = window_size + train_steps + validation_steps + test_steps
    
    # Definir el punto de inicio para cortar la serie temporal
    start = (len(ts) // segment_size_) * segment_size_
    ts0 = ts[-start:]
    
    fig, ax = plt.subplots(figsize=(12, 6))
    
    # Graficar toda la serie temporal
    ax.plot(range(len(ts)), ts, label='Serie Temporal Completa', color='lightgray')
    
    # Indicar el conjunto de entrenamiento, validación y prueba
    colors = {'train': 'blue', 'validation': 'orange', 'test': 'green'}
    
    i = 0
    count = 0
    while (len(ts0) - i + 1) >= segment_size_:
        # Ventanas de entrenamiento
        for step in range(train_steps):
            x_range = range(i, i + window_size)
            ax.plot(x_range, ts0[i:i + window_size], color=colors['train'], label='Entrenamiento' if count == 0 else "")
            i += 1
        
        # Ventanas de validación
        for step in range(validation_steps):
            x_range = range(i, i + window_size)
            ax.plot(x_range, ts0[i:i + window_size], color=colors['validation'], label='Validación' if count == 0 else "")
            i += 1
        
        # Ventanas de prueba
        for step in range(test_steps):
            x_range = range(i, i + window_size)
            ax.plot(x_range, ts0[i:i + window_size], color=colors['test'], label='Prueba' if count == 0 else "")
            i += 1
        
        count += 1

    # Añadir leyenda y título
    ax.legend(loc='upper right')
    ax.set_title(f'Visualización de ventanas deslizantes\nTamaño ventana: {window_size}, Pasos entrenamiento: {train_steps}, Validación: {validation_steps}, Prueba: {test_steps}')
    plt.xlabel('Índice de Tiempo')
    plt.ylabel('Valor de la Serie Temporal')
    plt.show()

# Crear una serie temporal simulada
ts = np.sin(np.linspace(0, 50, 300))  # Serie temporal de ejemplo

# Parámetros para la visualización
window_size = 10
train_steps = 5
validation_steps = 3
test_steps = 2

# Llamada a la función de visualización
visualize_windows(ts, window_size, train_steps, validation_steps, test_steps)

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches

def plot_windowing_structure(window_size, train_steps, validation_steps, test_steps, num_rows=10):
    fig, ax = plt.subplots(figsize=(12, 6))
    
    # Crear una serie temporal de ejemplo
    series_len = num_rows * (train_steps + validation_steps + test_steps)
    ts = np.arange(1, series_len + 1)
    
    # Definir colores
    train_color = 'red'
    val_color = 'blue'
    test_color = 'green'
    
    for row in range(num_rows):
        # Calcular la posición base de inicio para la fila
        start_pos = row * (train_steps + validation_steps + test_steps)
        
        # Entrenamiento
        for i in range(train_steps):
            x_start = start_pos + i
            ax.add_patch(patches.Rectangle((x_start, row), window_size, 1, edgecolor='none', facecolor=train_color))
        
        # Validación
        for i in range(train_steps, train_steps + validation_steps):
            x_start = start_pos + i
            ax.add_patch(patches.Rectangle((x_start, row), window_size, 1, edgecolor='none', facecolor=val_color))
        
        # Prueba
        for i in range(train_steps + validation_steps, train_steps + validation_steps + test_steps):
            x_start = start_pos + i
            ax.add_patch(patches.Rectangle((x_start, row), window_size, 1, edgecolor='none', facecolor=test_color))
    
    # Etiquetas y leyenda
    ax.set_xlim(0, series_len)
    ax.set_ylim(-1, num_rows)
    ax.set_xlabel('Índice de tiempo')
    ax.set_ylabel('Iteraciones (filas)')
    
    # Crear leyenda personalizada
    legend_handles = [
        patches.Patch(color=train_color, label='Entrenamiento'),
        patches.Patch(color=val_color, label='Validación'),
        patches.Patch(color=test_color, label='Prueba')
    ]
    ax.legend(handles=legend_handles)
    
    plt.title(f'Estructura de ventanas deslizantes: {window_size} pasos por ventana')
    plt.grid(False)
    plt.show()

# Parámetros de ventana
window_size = 7
train_steps = 14
validation_steps = 7
test_steps = 7

# Llamar a la función para graficar la estructura de las ventanas
plot_windowing_structure(window_size, train_steps, validation_steps, test_steps, num_rows=5)

import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.preprocessing import MinMaxScaler
from torch.utils.data import DataLoader, TensorDataset
from sklearn.metrics import r2_score
import itertools
import os
import yfinance as yf
import pandas as pd
import warnings
warnings.filterwarnings("ignore")
import numpy as np
from matplotlib import pyplot as plt
import seaborn as sns
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error, r2_score
from scipy.stats import kurtosis, skew, jarque_bera
from statsmodels.tsa.stattools import adfuller, kpss
import matplotlib.pyplot as plt
import seaborn as sns
import statsmodels.api as sm
from scipy.stats import kurtosistest, skewtest, jarque_bera
from statsmodels.tsa.arima.model import ARIMA

# Function to calculate MAPE, RMSE, and R² adj
def calculate_metrics(y_true, y_pred, n, p):
    y_true = y_true.flatten()
    y_pred = y_pred.flatten()
    mape = np.mean(np.abs((y_true - y_pred) / y_true)) * 100
    rmse = np.sqrt(np.mean((y_true - y_pred) ** 2))
    ss_res = np.sum((y_true - y_pred) ** 2)
    ss_tot = np.sum((y_true - np.mean(y_true)) ** 2)
    r2 = 1 - (ss_res / ss_tot)
    r2_adj = 1 - ((1 - r2) * (n - 1) / (n - p - 1))
    return mape, rmse, r2, r2_adj

# Function to evaluate the model and create a dataframe row
def evaluate_and_create_row(model, data_loader, criterion, scaler, window_size, model_name):
    model.eval()
    all_predictions = []
    all_targets = []
    with torch.no_grad():
        for X_batch, y_batch in data_loader:
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)

    # Concatenate all predictions and targets
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy()
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy()

    all_predictions = scaler.inverse_transform(all_predictions.reshape(-1, 1))
    all_targets = scaler.inverse_transform(all_targets.reshape(-1, 1))

    n = len(all_targets)
    p = window_size
    mape, rmse, r2, r2_adj = calculate_metrics(np.concatenate(all_targets), np.concatenate(all_predictions), n, p)

    metrics_df = pd.DataFrame({
        'Model': [model_name],
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })

    return all_predictions, all_targets, metrics_df

class LSTMModel(nn.Module):
    def __init__(self, input_size, hidden_size, output_size, num_layers):
        super(LSTMModel, self).__init__()
        self.num_layers = num_layers
        self.hidden_size = hidden_size
        self.lstm = nn.LSTM(input_size, hidden_size, num_layers, batch_first=True)
        self.fc = nn.Linear(hidden_size, output_size)

    def forward(self, x):
        h_0 = torch.zeros(self.num_layers, x.size(0), self.hidden_size).to(x.device)
        c_0 = torch.zeros(self.num_layers, x.size(0), self.hidden_size).to(x.device)

        out, _ = self.lstm(x, (h_0, c_0))
        out = self.fc(out)  # Apply fully connected layer to each time step
        return out

import pandas as pd
import numpy as np
from statsmodels.graphics.tsaplots import plot_acf
import matplotlib.pyplot as plt
from statsmodels.api import qqplot
from statsmodels.tsa.stattools import acf
from statsmodels.stats.diagnostic import normal_ad
from scipy import stats

# Normalize the data
# Ruta del archivo CSV
BHdata = "C:\\Users\\Maestriadatos\\Documents\\lizcanollerenaparcial\\docs\\bitcoinhistoricaldata.csv"
df = pd.read_csv(BHdata)
# Convertir la columna 'Price', 'Open', 'High', 'Low' eliminando comas y convirtiendo a float
df['Price'] = df['Price'].str.replace(',', '').astype(float)
df['Open'] = df['Open'].str.replace(',', '').astype(float)
df['High'] = df['High'].str.replace(',', '').astype(float)
df['Low'] = df['Low'].str.replace(',', '').astype(float)

# Convertir la columna 'Vol.' eliminando comas, reemplazando 'K' por 'e3' (miles) y 'M' por 'e6' (millones), luego convertir a numérico
df['Vol.'] = df['Vol.'].str.replace('K', 'e3').str.replace('M', 'e6').str.replace(',', '')
df['Vol.'] = pd.to_numeric(df['Vol.'], errors='coerce')

# Convertir la columna 'Change %' eliminando el símbolo '%' y convirtiendo a float
df['Change %'] = df['Change %'].str.replace('%', '').astype(float)
# Cargar los datos
scaler = MinMaxScaler(feature_range=(0, 1))
btc_close_scaled = scaler.fit_transform(df.Price.values.reshape(-1, 1))

# Convert to tensor
btc_close_tensor = torch.FloatTensor(btc_close_scaled).view(-1)
shared_folder_path = "C:\\Users\\Maestriadatos\\Documents\\lizcanollerenaparcial\\docs"
files = os.listdir(shared_folder_path)
print(files)

['.git', 'bitcoinhistoricaldata.csv', 'intro.md', 'logo.png', 'lstm_modelAt_14_14.pth', 'lstm_modelAt_14_21.pth', 'lstm_modelAt_14_28.pth', 'lstm_modelAt_14_7.pth', 'lstm_modelAt_21_14.pth', 'lstm_modelAt_21_21.pth', 'lstm_modelAt_21_28.pth', 'lstm_modelAt_21_7.pth', 'lstm_modelAt_28_14.pth', 'lstm_modelAt_28_21.pth', 'lstm_modelAt_28_28.pth', 'lstm_modelAt_28_7.pth', 'lstm_modelAt_7_14.pth', 'lstm_modelAt_7_21.pth', 'lstm_modelAt_7_28.pth', 'lstm_modelAt_7_7.pth', 'lstm_modelVol7_14_14.pth', 'lstm_modelVol7_14_21.pth', 'lstm_modelVol7_14_28.pth', 'lstm_modelVol7_14_7.pth', 'lstm_modelVol7_21_14.pth', 'lstm_modelVol7_21_21.pth', 'lstm_modelVol7_21_28.pth', 'lstm_modelVol7_21_7.pth', 'lstm_modelVol7_28_14.pth', 'lstm_modelVol7_28_21.pth', 'lstm_modelVol7_28_28.pth', 'lstm_modelVol7_28_7.pth', 'lstm_modelVol7_7_14.pth', 'lstm_modelVol7_7_21.pth', 'lstm_modelVol7_7_28.pth', 'lstm_modelVol7_7_7.pth', 'lstm_model_14_14.pth', 'lstm_model_14_21.pth', 'lstm_model_14_28.pth', 'lstm_model_14_7.pth', 'lstm_model_21_14.pth', 'lstm_model_21_21.pth', 'lstm_model_21_28.pth', 'lstm_model_21_7.pth', 'lstm_model_28_14.pth', 'lstm_model_28_21.pth', 'lstm_model_28_28.pth', 'lstm_model_28_7.pth', 'lstm_model_7_14.pth', 'lstm_model_7_21.pth', 'lstm_model_7_28.pth', 'lstm_model_7_7.pth', 'markdown-notebooks.md', 'markdown.md', 'mlp_model_14_14.pth', 'mlp_model_14_21.pth', 'mlp_model_14_28.pth', 'mlp_model_14_7.pth', 'mlp_model_21_14.pth', 'mlp_model_21_21.pth', 'mlp_model_21_28.pth', 'mlp_model_21_7.pth', 'mlp_model_28_14.pth', 'mlp_model_28_21.pth', 'mlp_model_28_28.pth', 'mlp_model_28_7.pth', 'mlp_model_7_14.pth', 'mlp_model_7_21.pth', 'mlp_model_7_28.pth', 'mlp_model_7_7.pth', 'notebooks.ipynb', 'references.bib', 'requirements.txt', 'rnn_modelAt_14_14.pth', 'rnn_modelAt_14_21.pth', 'rnn_modelAt_14_28.pth', 'rnn_modelAt_14_7.pth', 'rnn_modelAt_21_14.pth', 'rnn_modelAt_21_21.pth', 'rnn_modelAt_21_28.pth', 'rnn_modelAt_21_7.pth', 'rnn_modelAt_28_14.pth', 'rnn_modelAt_28_21.pth', 'rnn_modelAt_28_28.pth', 'rnn_modelAt_28_7.pth', 'rnn_modelAt_7_14.pth', 'rnn_modelAt_7_21.pth', 'rnn_modelAt_7_28.pth', 'rnn_modelAt_7_7.pth', 'rnn_modelVol_14_14.pth', 'rnn_modelVol_14_21.pth', 'rnn_modelVol_14_28.pth', 'rnn_modelVol_14_7.pth', 'rnn_modelVol_21_14.pth', 'rnn_modelVol_21_21.pth', 'rnn_modelVol_21_28.pth', 'rnn_modelVol_21_7.pth', 'rnn_modelVol_28_14.pth', 'rnn_modelVol_28_21.pth', 'rnn_modelVol_28_28.pth', 'rnn_modelVol_28_7.pth', 'rnn_modelVol_7_14.pth', 'rnn_modelVol_7_21.pth', 'rnn_modelVol_7_28.pth', 'rnn_modelVol_7_7.pth', 'rnn_model_14_14.pth', 'rnn_model_14_21.pth', 'rnn_model_14_28.pth', 'rnn_model_14_7.pth', 'rnn_model_21_14.pth', 'rnn_model_21_21.pth', 'rnn_model_21_28.pth', 'rnn_model_21_7.pth', 'rnn_model_28_14.pth', 'rnn_model_28_21.pth', 'rnn_model_28_28.pth', 'rnn_model_28_7.pth', 'rnn_model_7_14.pth', 'rnn_model_7_21.pth', 'rnn_model_7_28.pth', 'rnn_model_7_7.pth', '_build', '_config.yml', '_toc.yml']

window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]

columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']

lstm_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):
    # Create windows
    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'lstm_model_{window_size}_{train_steps}.pth'

    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        lstm_result_df = pd.concat([lstm_result_df, valid_metrics_df], ignore_index=True)
        continue

    validation_steps = 14
    test_steps = 14

    # Create windows
    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_close_tensor, window_size, train_steps, validation_steps, test_steps)

    # Reshape the data to match the required input shape
    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)


    train_dataset = TensorDataset(Xtrains, ytrains)
    valid_dataset = TensorDataset(Xvalids, yvalids)
    test_dataset = TensorDataset(Xtests, ytests)

    # batch_size = Xtrains.shape[0]  # Ensure batch_size matches the first dimension of Xtrains
    batch_size = 1
    train_loader_original = DataLoader(train_dataset, batch_size=batch_size, shuffle=False)
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(valid_dataset, batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(test_dataset, batch_size=batch_size, shuffle=False)


    # Model Parameters
    input_size = window_size
    hidden_size = 25
    output_size = 1
    num_layers = 6

    model = LSTMModel(input_size, hidden_size, output_size, num_layers).to(device)

    # Training parameters
    num_epochs = 100
    learning_rate = 0.001

    # Loss and optimizer
    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

    # Training loop
    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()  # Zero out the gradients for the next batch
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()  # Backpropagation
            optimizer.step()  # Optimize the weights
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)

    lstm_result_df = pd.concat([lstm_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'state_dict': model.state_dict(),
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df
    }, os.path.join(shared_folder_path, model_name))

    print("Model saved successfully!")

Device: cpu
Window Size: 7, Training Step Size: 7
Window Size: 7, Training Step Size: 14
Window Size: 7, Training Step Size: 21
Window Size: 7, Training Step Size: 28
Window Size: 14, Training Step Size: 7
Window Size: 14, Training Step Size: 14
Window Size: 14, Training Step Size: 21
Window Size: 14, Training Step Size: 28
Window Size: 21, Training Step Size: 7
Window Size: 21, Training Step Size: 14
Window Size: 21, Training Step Size: 21
Window Size: 21, Training Step Size: 28
Window Size: 28, Training Step Size: 7
Window Size: 28, Training Step Size: 14
Window Size: 28, Training Step Size: 21
Window Size: 28, Training Step Size: 28

# Model Parameters
input_size = window_size
hidden_size = 25
output_size = 1
num_layers = 6

model_with_min_r2_adj = lstm_result_df.loc[lstm_result_df['R² adj'].idxmax(), 'Model']
print(f"Model with the smallest R² adjusted: {model_with_min_r2_adj}")
model = LSTMModel(input_size, hidden_size, output_size, num_layers).to(device)

checkpoint = torch.load(os.path.join(shared_folder_path, model_with_min_r2_adj))

input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

lstm_model = LSTMModel(input_size, hidden_size, output_size, num_layers)

lstm_model.load_state_dict(checkpoint['state_dict'])
lstm_model.to(device)
print("Model loaded successfully!")

Model with the smallest R² adjusted: lstm_model_14_21.pth
Model loaded successfully!

lstm_result_df

	Model	MAPE	RMSE	R²	R² adj
0	lstm_model_7_7.pth	13823.792969	3889.401367	0.939962	0.939749
1	lstm_model_7_14.pth	8316.774414	1277.516479	0.993282	0.993254
2	lstm_model_7_21.pth	9519.721680	2633.489014	0.970614	0.970467
3	lstm_model_7_28.pth	8158.646484	1525.957520	0.989754	0.989695
4	lstm_model_14_7.pth	9025.233398	2417.115479	0.975942	0.975771
5	lstm_model_14_14.pth	3142.239990	954.562744	0.996184	0.996151
6	lstm_model_14_21.pth	2346.378418	911.253235	0.996390	0.996354
7	lstm_model_14_28.pth	8347.414062	1983.402710	0.982615	0.982415
8	lstm_model_21_7.pth	10256.427734	2825.454102	0.966234	0.965871
9	lstm_model_21_14.pth	23891.451172	1722.454346	0.987155	0.986990
10	lstm_model_21_21.pth	20530.283203	1048.479858	0.995303	0.995233
11	lstm_model_21_28.pth	6618.501953	1443.454102	0.990350	0.990180
12	lstm_model_28_7.pth	35114.261719	2558.657227	0.971567	0.971158
13	lstm_model_28_14.pth	13888.269531	2208.796875	0.978633	0.978261
14	lstm_model_28_21.pth	18652.074219	1173.737305	0.993867	0.993742
15	lstm_model_28_28.pth	23398.820312	1144.378540	0.994465	0.994336

En los resultados obtenidos con los modelos LSTM para la predicción del precio de Bitcoin, se puede notar que el rendimiento varía significativamente en función del tamaño de la ventana y el horizonte de predicción. En general, los modelos con una ventana de 14 días tienden a ofrecer las mejores métricas, como el caso del modelo con ventana y horizonte de 14 días (lstm_model_14_14.pth) que obtuvo el MAPE más bajo (3142.24) y un R² cercano a 1 (0.996184), lo que indica una alta precisión en sus predicciones.

Los modelos con ventanas de 7 y 21 días también muestran buenos resultados, pero hay más variabilidad en el error. Por ejemplo, el modelo con ventana de 7 días y horizonte de 14 (lstm_model_7_14.pth) presenta un error menor (MAPE de 8316.77) en comparación con el mismo modelo con horizonte de 21 días (lstm_model_7_21.pth), que tiene un MAPE mayor (9519.72).

Finalmente, los modelos con ventanas de 28 días tienen más dificultad para mantener una precisión constante, especialmente en los horizontes más cortos, como se observa en el modelo lstm_model_28_7.pth, que tiene un MAPE muy elevado (35114.26), lo que indica una menor capacidad para capturar las variaciones del precio en esos intervalos.

# Loss and optimizer
criterion = nn.MSELoss()


def count_parameters(model):
    return sum(p.numel() for p in model.parameters() if p.requires_grad)

def calculate_adjusted_r2(all_targets, all_predictions, model):
    n = len(all_targets)
    k = count_parameters(model)  # Total number of trainable parameters

    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (n - 1) / (n - k - 1)

    print(f"R²: {r2:.4f}")
    print(f"R² adjusted: {r2_adj:.4f}")
    print(f"Number of trainable parameters: {k}")
    print(f"Nunmber of measures : {n}")

    return r2_adj

def evaluate_model_residues(model, data_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    with torch.no_grad():
        for X_batch, y_batch in data_loader:
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)

    # Concatenate all predictions and targets
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)

    residues = all_targets - all_predictions

    # Calculate statistics
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)

    kurt_stat, kurt_p_value = kurtosistest(residues)
    skew_stat, skew_p_value = skewtest(residues)
    jb_stat, jb_p_value = jarque_bera(residues)
    adf_stat, adf_p_value, _, _, _, _ = adfuller(residues)
    kpss_stat, kpss_p_value, _, _ = kpss(residues)

    results = {
        'MAPE': mape,
        'RMSE': rmse,
        # 'R2 adj': r2_adj,
        'R2': r2,
        'Kurtosis (statistic)': kurt_stat,
        'Kurtosis (p-value)': kurt_p_value,
        'Skewness (statistic)': skew_stat,
        'Skewness (p-value)': skew_p_value,
        'Jarque-Bera (statistic)': jb_stat,
        'Jarque-Bera (p-value)': jb_p_value,
        'Dickey Fuller (statistic)': adf_stat,
        'Dickey Fuller (p-value)': adf_p_value,
        'KPSS test (statistic)': kpss_stat,
        'KPSS test (p-value)': kpss_p_value
    }

    results_df = pd.DataFrame.from_dict(results, orient='index', columns=['Value'])

    # Plotting the time series of residues
    plt.figure(figsize=(10, 6))
    plt.plot(residues)
    plt.title('Time Series of Residues')
    plt.xlabel('Time')
    plt.ylabel('Residues')
    plt.show()

    # Plotting the histogram of residues
    plt.figure(figsize=(10, 6))
    sns.histplot(residues, kde=True)
    plt.title('Histogram of Residues')
    plt.xlabel('Residues')
    plt.ylabel('Frequency')
    plt.show()

    # Q-Q plot of residues
    plt.figure(figsize=(10, 6))
    sm.qqplot(residues, line='s')
    plt.title('Q-Q Plot of Residues')
    plt.show()

    # ACF plot of residues
    plt.figure(figsize=(10, 6))
    sm.graphics.tsa.plot_acf(residues, lags=40)
    plt.title('Autocorrelation Function (ACF) of Residues')
    plt.show()

    return residues, results_df

residues, results_df = evaluate_model_residues(lstm_model, test_loader, criterion)
results_df

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

	Value
MAPE	9.413034e+10
RMSE	1.179102e-02
R2	9.968290e-01
Kurtosis (statistic)	1.727034e+01
Kurtosis (p-value)	7.867481e-67
Skewness (statistic)	-1.122920e+01
Skewness (p-value)	2.931350e-29
Jarque-Bera (statistic)	1.030804e+04
Jarque-Bera (p-value)	0.000000e+00
Dickey Fuller (statistic)	-8.623177e+00
Dickey Fuller (p-value)	6.027746e-14
KPSS test (statistic)	3.385352e-01
KPSS test (p-value)	1.000000e-01

Analisis del las graficas

Al analizar los residuos de la red neuronal LSTM aplicada a la serie de tiempo de precios, comienzo observando el gráfico de los residuos en función del tiempo. Se puede notar que los residuos presentan una alta concentración al inicio, lo que podría indicar que el modelo tiene dificultades en ajustar la serie en las primeras etapas. Sin embargo, a medida que avanza el tiempo, esta concentración disminuye, lo que sugiere una mejoría en el ajuste del modelo en los periodos posteriores.

El histograma de los residuos muestra una distribución que, a simple vista, parece normal, lo cual en principio es un indicador favorable para la capacidad predictiva del modelo. No obstante, se observa una columna central significativamente alta, lo que indica una concentración de valores en torno al cero. Esto podría señalar que el modelo subestima la variabilidad real de la serie de precios o que existen ciertos patrones persistentes en los residuos no capturados por la LSTM.

El QQ plot, que normalmente ayuda a verificar si los residuos siguen una distribución normal, revela una disposición sinusoidal de los puntos alrededor de la línea de referencia central. Este patrón indica la presencia de colas más pesadas o algún tipo de asimetría en los residuos, desviándose de la normalidad. La forma sinusoidal sugiere la presencia de patrones cíclicos o dependencias no capturadas adecuadamente por el modelo.

Por último, la prueba ACF muestra tres rezagos fuera de la banda de significancia, lo cual sugiere una autocorrelación residual en dichos puntos. Esto es indicativo de que el modelo no ha logrado eliminar por completo la dependencia temporal en los datos, lo que podría implicar la necesidad de ajustar hiperparámetros, aumentar la complejidad del modelo o probar alguna transformación adicional en los datos.

En conjunto, estos gráficos sugieren que, si bien el modelo captura algunos patrones en la serie de precios, aún existen dependencias y patrones no ajustados completamente. Estos hallazgos me llevan a considerar ajustes adicionales en la arquitectura del modelo o en los preprocesamientos aplicados a la serie para mejorar la capacidad predictiva y reducir la dependencia residual.

Analisis de las pruebas

Al analizar los residuos de la predicción de mi modelo LSTM para el precio del Bitcoin, encuentro resultados mixtos. El 𝑅 2 R 2 de 0.9968 indica un ajuste sólido, y el RMSE bajo de 0.0118 muestra que los errores absolutos son pequeños en términos relativos. Sin embargo, el MAPE extremadamente alto ( 9.41 × 1 0 10 9.41×10 10 ) sugiere que el modelo presenta problemas al generalizar, especialmente en valores extremos. La distribución de los residuos muestra una kurtosis elevada (17.27) y una asimetría negativa fuerte (-11.23), lo que refleja colas pesadas y sesgo negativo, indicando que el modelo subestima algunos valores. La prueba de Jarque-Bera confirma la falta de normalidad, lo cual sugiere errores no aleatorios que pueden afectar la robustez del modelo frente a valores atípicos. Afortunadamente, las pruebas de estacionariedad, tanto Dickey-Fuller como KPSS, indican que los residuos son estacionarios, lo cual es positivo para la estabilidad del modelo en el tiempo.

test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(lstm_model, test_loader, criterion, scaler, window_size, "LSTM")
plt.plot(test_predictions.reshape(-1), label='test_predictions')
plt.plot(test_targets.reshape(-1), label='test_targets')
plt.legend()
plt.show()
test_metrics_df

	Model	MAPE	RMSE	R²	R² adj
0	LSTM	2427.556885	861.525208	0.996829	0.996765

Al observar el gráfico de predicción en el conjunto de validación, se puede ver que el modelo LSTM logra un ajuste notablemente preciso. Las predicciones siguen de cerca el comportamiento de los datos reales, lo que indica que el modelo ha capturado adecuadamente los patrones principales de la serie de precios en el periodo de validación. Esta precisión en el ajuste es un buen indicador de que el modelo es capaz de generalizar, al menos en los datos de validación, lo que respalda su utilidad en aplicaciones futuras.

Sin embargo, los análisis previos de los residuos sugieren que aún quedan áreas por mejorar. Aunque la predicción en el conjunto de validación es prometedora, la persistencia de patrones cíclicos y autocorrelaciones en los residuos, junto con la fuerte concentración de valores en torno al cero, señala posibles ajustes necesarios para mejorar la robustez del modelo y su capacidad para capturar variaciones menores o patrones complejos en el tiempo.

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
lstm_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for LSTM Model")
plt.grid()
plt.show()

LSTM Retornos acumulados

# Eliminar las filas con valores nulos en la columna 'Price'
df.dropna(subset=['Price'], inplace=True)

# Calcular el retorno diario Rt
df['Rt'] = (df['Price'] - df['Price'].shift(1)) / df['Price'].shift(1)

# Calcular el retorno acumulado diario At
df['At'] = df['Rt'].cumsum()

# Función para calcular la volatilidad usando ventanas móviles
def calcular_volatilidad(data, ventana):
    """
    Esta función calcula la volatilidad (desviación estándar) 
    de los retornos diarios utilizando una ventana móvil.
    """
    return data['Rt'].rolling(window=ventana).std()

# Calcular volatilidad para diferentes ventanas
ventanas = [7, 14, 21, 28]
for ventana in ventanas:
    df[f'Volatilidad_{ventana}'] = calcular_volatilidad(df, ventana)



# Cargar los datos
scaler = MinMaxScaler(feature_range=(0, 1))
btc_At_scaled = scaler.fit_transform(df.At.values.reshape(-1, 1))

# Convert to tensor
btc_At_tensor = torch.FloatTensor(btc_At_scaled).view(-1)
shared_folder_path = "C:\\Users\\Maestriadatos\\Documents\\lizcanollerenaparcial\\docs"
files = os.listdir(shared_folder_path)
print(files)

['.git', 'bitcoinhistoricaldata.csv', 'intro.md', 'logo.png', 'lstm_modelAt_14_14.pth', 'lstm_modelAt_14_21.pth', 'lstm_modelAt_14_28.pth', 'lstm_modelAt_14_7.pth', 'lstm_modelAt_21_14.pth', 'lstm_modelAt_21_21.pth', 'lstm_modelAt_21_28.pth', 'lstm_modelAt_21_7.pth', 'lstm_modelAt_28_14.pth', 'lstm_modelAt_28_21.pth', 'lstm_modelAt_28_28.pth', 'lstm_modelAt_28_7.pth', 'lstm_modelAt_7_14.pth', 'lstm_modelAt_7_21.pth', 'lstm_modelAt_7_28.pth', 'lstm_modelAt_7_7.pth', 'lstm_modelVol7_14_14.pth', 'lstm_modelVol7_14_21.pth', 'lstm_modelVol7_14_28.pth', 'lstm_modelVol7_14_7.pth', 'lstm_modelVol7_21_14.pth', 'lstm_modelVol7_21_21.pth', 'lstm_modelVol7_21_28.pth', 'lstm_modelVol7_21_7.pth', 'lstm_modelVol7_28_14.pth', 'lstm_modelVol7_28_21.pth', 'lstm_modelVol7_28_28.pth', 'lstm_modelVol7_28_7.pth', 'lstm_modelVol7_7_14.pth', 'lstm_modelVol7_7_21.pth', 'lstm_modelVol7_7_28.pth', 'lstm_modelVol7_7_7.pth', 'lstm_model_14_14.pth', 'lstm_model_14_21.pth', 'lstm_model_14_28.pth', 'lstm_model_14_7.pth', 'lstm_model_21_14.pth', 'lstm_model_21_21.pth', 'lstm_model_21_28.pth', 'lstm_model_21_7.pth', 'lstm_model_28_14.pth', 'lstm_model_28_21.pth', 'lstm_model_28_28.pth', 'lstm_model_28_7.pth', 'lstm_model_7_14.pth', 'lstm_model_7_21.pth', 'lstm_model_7_28.pth', 'lstm_model_7_7.pth', 'markdown-notebooks.md', 'markdown.md', 'mlp_model_14_14.pth', 'mlp_model_14_21.pth', 'mlp_model_14_28.pth', 'mlp_model_14_7.pth', 'mlp_model_21_14.pth', 'mlp_model_21_21.pth', 'mlp_model_21_28.pth', 'mlp_model_21_7.pth', 'mlp_model_28_14.pth', 'mlp_model_28_21.pth', 'mlp_model_28_28.pth', 'mlp_model_28_7.pth', 'mlp_model_7_14.pth', 'mlp_model_7_21.pth', 'mlp_model_7_28.pth', 'mlp_model_7_7.pth', 'notebooks.ipynb', 'references.bib', 'requirements.txt', 'rnn_modelAt_14_14.pth', 'rnn_modelAt_14_21.pth', 'rnn_modelAt_14_28.pth', 'rnn_modelAt_14_7.pth', 'rnn_modelAt_21_14.pth', 'rnn_modelAt_21_21.pth', 'rnn_modelAt_21_28.pth', 'rnn_modelAt_21_7.pth', 'rnn_modelAt_28_14.pth', 'rnn_modelAt_28_21.pth', 'rnn_modelAt_28_28.pth', 'rnn_modelAt_28_7.pth', 'rnn_modelAt_7_14.pth', 'rnn_modelAt_7_21.pth', 'rnn_modelAt_7_28.pth', 'rnn_modelAt_7_7.pth', 'rnn_modelVol_14_14.pth', 'rnn_modelVol_14_21.pth', 'rnn_modelVol_14_28.pth', 'rnn_modelVol_14_7.pth', 'rnn_modelVol_21_14.pth', 'rnn_modelVol_21_21.pth', 'rnn_modelVol_21_28.pth', 'rnn_modelVol_21_7.pth', 'rnn_modelVol_28_14.pth', 'rnn_modelVol_28_21.pth', 'rnn_modelVol_28_28.pth', 'rnn_modelVol_28_7.pth', 'rnn_modelVol_7_14.pth', 'rnn_modelVol_7_21.pth', 'rnn_modelVol_7_28.pth', 'rnn_modelVol_7_7.pth', 'rnn_model_14_14.pth', 'rnn_model_14_21.pth', 'rnn_model_14_28.pth', 'rnn_model_14_7.pth', 'rnn_model_21_14.pth', 'rnn_model_21_21.pth', 'rnn_model_21_28.pth', 'rnn_model_21_7.pth', 'rnn_model_28_14.pth', 'rnn_model_28_21.pth', 'rnn_model_28_28.pth', 'rnn_model_28_7.pth', 'rnn_model_7_14.pth', 'rnn_model_7_21.pth', 'rnn_model_7_28.pth', 'rnn_model_7_7.pth', '_build', '_config.yml', '_toc.yml']

window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]

columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']

lstm_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):
    # Create windows
    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'lstm_modelAt_{window_size}_{train_steps}.pth'

    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        lstm_result_df = pd.concat([lstm_result_df, valid_metrics_df], ignore_index=True)
        continue

    validation_steps = 14
    test_steps = 14

    # Create windows
    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_At_tensor, window_size, train_steps, validation_steps, test_steps)

    # Reshape the data to match the required input shape
    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)


    train_dataset = TensorDataset(Xtrains, ytrains)
    valid_dataset = TensorDataset(Xvalids, yvalids)
    test_dataset = TensorDataset(Xtests, ytests)

    # batch_size = Xtrains.shape[0]  # Ensure batch_size matches the first dimension of Xtrains
    batch_size = 16
    train_loader_original = DataLoader(train_dataset, batch_size=batch_size, shuffle=False)
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(valid_dataset, batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(test_dataset, batch_size=batch_size, shuffle=False)


    # Model Parameters
    input_size = window_size
    hidden_size = 5
    output_size = 1
    num_layers = 6

    model = LSTMModel(input_size, hidden_size, output_size, num_layers).to(device)

    # Training parameters
    num_epochs = 100
    learning_rate = 0.001

    # Loss and optimizer
    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

    # Training loop
    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()  # Zero out the gradients for the next batch
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()  # Backpropagation
            optimizer.step()  # Optimize the weights
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)

    lstm_result_dfAt = pd.concat([lstm_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'state_dict': model.state_dict(),
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df
    }, os.path.join(shared_folder_path, model_name))

    print("Model saved successfully!")

Device: cpu
Window Size: 7, Training Step Size: 7
Window Size: 7, Training Step Size: 14
Window Size: 7, Training Step Size: 21
Window Size: 7, Training Step Size: 28
Window Size: 14, Training Step Size: 7
Window Size: 14, Training Step Size: 14
Window Size: 14, Training Step Size: 21
Window Size: 14, Training Step Size: 28
Window Size: 21, Training Step Size: 7
Window Size: 21, Training Step Size: 14
Window Size: 21, Training Step Size: 21
Window Size: 21, Training Step Size: 28
Window Size: 28, Training Step Size: 7
Window Size: 28, Training Step Size: 14
Window Size: 28, Training Step Size: 21
Window Size: 28, Training Step Size: 28

lstm_result_df

	Model	MAPE	RMSE	R²	R² adj
0	lstm_modelAt_7_7.pth	76.911530	0.308117	0.944188	0.943991
1	lstm_modelAt_7_14.pth	73.137489	0.524841	0.836854	0.836160
2	lstm_modelAt_7_21.pth	228.004532	0.879214	0.543819	0.541548
3	lstm_modelAt_7_28.pth	294.488953	1.497455	-0.344227	-0.351914
4	lstm_modelAt_14_7.pth	115.428879	0.835289	0.590325	0.587418
5	lstm_modelAt_14_14.pth	78.023338	0.372065	0.917499	0.916794
6	lstm_modelAt_14_21.pth	176.888351	0.757989	0.658089	0.654667
7	lstm_modelAt_14_28.pth	201.702637	0.509021	0.847431	0.845676
8	lstm_modelAt_21_7.pth	96.139023	0.355213	0.924604	0.923793
9	lstm_modelAt_21_14.pth	100.701965	0.468056	0.871907	0.870257
10	lstm_modelAt_21_21.pth	101.409386	0.703727	0.710726	0.706362
11	lstm_modelAt_21_28.pth	355.159363	1.482051	-0.311112	-0.334133
12	lstm_modelAt_28_7.pth	76.436249	0.355997	0.925336	0.924261
13	lstm_modelAt_28_14.pth	121.831467	0.547822	0.821311	0.818202
14	lstm_modelAt_28_21.pth	130.495758	0.669949	0.737431	0.732068
15	lstm_modelAt_28_28.pth	302.191559	0.956602	0.462024	0.449503

En los resultados de los modelos LSTM para la predicción de los retornos acumulados del Bitcoin, se observa un comportamiento desigual dependiendo del tamaño de la ventana y del horizonte de predicción. Los modelos con ventanas de 7 y 28 días presentan un buen desempeño en horizontes cortos, con MAPE relativamente bajos, como en el caso del modelo lstm_modelAt_7_7.pth (MAPE de 76.91 y R² de 0.944) y el lstm_modelAt_28_7.pth (MAPE de 76.44 y R² de 0.925).

Sin embargo, los horizontes más largos, especialmente en ventanas de 7 y 21 días, presentan una clara degradación en la precisión. Por ejemplo, el modelo lstm_modelAt_7_28.pth tiene un MAPE elevado (294.49) y un R² negativo (-0.344), lo que sugiere que no está capturando bien las tendencias.

En contraste, el modelo lstm_modelAt_14_14.pth muestra un equilibrio sólido entre precisión y error (MAPE de 78.02 y R² de 0.917), lo que sugiere que una ventana de 14 días es adecuada para predecir con mayor precisión en horizontes intermedios.

En general, los resultados indican que el rendimiento es más estable en horizontes más cortos, mientras que en horizontes largos los errores crecen significativamente, especialmente con ventanas pequeñas como de 7 días.

model_with_min_r2_adj = lstm_result_df.loc[lstm_result_df['R² adj'].idxmax(), 'Model']
print(f"Model with the smallest R² adjusted: {model_with_min_r2_adj}")

checkpoint = torch.load(os.path.join(shared_folder_path, model_with_min_r2_adj))

input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

lstm_model = LSTMModel(input_size, hidden_size, output_size, num_layers)

lstm_model.load_state_dict(checkpoint['state_dict'])
lstm_model.to(device)
print("Model loaded successfully!")

Model with the smallest R² adjusted: lstm_modelAt_7_7.pth
Model loaded successfully!

def count_parameters(model):
    return sum(p.numel() for p in model.parameters() if p.requires_grad)

def calculate_adjusted_r2(all_targets, all_predictions, model):
    n = len(all_targets)
    k = count_parameters(model)  # Total number of trainable parameters

    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (n - 1) / (n - k - 1)

    print(f"R²: {r2:.4f}")
    print(f"R² adjusted: {r2_adj:.4f}")
    print(f"Number of trainable parameters: {k}")
    print(f"Nunmber of measures : {n}")

    return r2_adj

def evaluate_model_residues(model, data_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    with torch.no_grad():
        for X_batch, y_batch in data_loader:
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)

    # Concatenate all predictions and targets
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)

    residues = all_targets - all_predictions

    # Calculate statistics
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)

    kurt_stat, kurt_p_value = kurtosistest(residues)
    skew_stat, skew_p_value = skewtest(residues)
    jb_stat, jb_p_value = jarque_bera(residues)
    adf_stat, adf_p_value, _, _, _, _ = adfuller(residues)
    kpss_stat, kpss_p_value, _, _ = kpss(residues)

    results = {
        'MAPE': mape,
        'RMSE': rmse,
        # 'R2 adj': r2_adj,
        'R2': r2,
        'Kurtosis (statistic)': kurt_stat,
        'Kurtosis (p-value)': kurt_p_value,
        'Skewness (statistic)': skew_stat,
        'Skewness (p-value)': skew_p_value,
        'Jarque-Bera (statistic)': jb_stat,
        'Jarque-Bera (p-value)': jb_p_value,
        'Dickey Fuller (statistic)': adf_stat,
        'Dickey Fuller (p-value)': adf_p_value,
        'KPSS test (statistic)': kpss_stat,
        'KPSS test (p-value)': kpss_p_value
    }

    results_df = pd.DataFrame.from_dict(results, orient='index', columns=['Value'])

    # Plotting the time series of residues
    plt.figure(figsize=(10, 6))
    plt.plot(residues)
    plt.title('Time Series of Residues')
    plt.xlabel('Time')
    plt.ylabel('Residues')
    plt.show()

    # Plotting the histogram of residues
    plt.figure(figsize=(10, 6))
    sns.histplot(residues, kde=True)
    plt.title('Histogram of Residues')
    plt.xlabel('Residues')
    plt.ylabel('Frequency')
    plt.show()

    # Q-Q plot of residues
    plt.figure(figsize=(10, 6))
    sm.qqplot(residues, line='s')
    plt.title('Q-Q Plot of Residues')
    plt.show()

    # ACF plot of residues
    plt.figure(figsize=(10, 6))
    sm.graphics.tsa.plot_acf(residues, lags=40)
    plt.title('Autocorrelation Function (ACF) of Residues')
    plt.show()

    return residues, results_df

residues, results_df = evaluate_model_residues(lstm_model, test_loader, criterion)
results_df

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

	Value
MAPE	1.129741e-01
RMSE	5.282082e-02
R2	9.442247e-01
Kurtosis (statistic)	1.152170e+01
Kurtosis (p-value)	1.025685e-30
Skewness (statistic)	-1.131176e+01
Skewness (p-value)	1.147666e-29
Jarque-Bera (statistic)	7.737599e+02
Jarque-Bera (p-value)	9.553780e-169
Dickey Fuller (statistic)	-5.154163e+00
Dickey Fuller (p-value)	1.089810e-05
KPSS test (statistic)	1.750138e+00
KPSS test (p-value)	1.000000e-02

Analisis de las graficas

Al analizar los residuos de la red neuronal LSTM aplicada a la serie de tiempo de los retornos acumulados de Bitcoin, el primer gráfico muestra los residuos en función del tiempo, donde se observa una alta variación al inicio que parece disminuir progresivamente. Esto indica que, en las etapas iniciales, el modelo tiene dificultades para ajustar las fluctuaciones de los retornos, probablemente debido a la naturaleza volátil de estos. Esta variación decreciente podría sugerir que el modelo LSTM mejora su ajuste en los periodos posteriores, adaptándose mejor a las tendencias de los retornos acumulados.

En el histograma de los residuos, se aprecia una distribución que se ajusta muy bien a la curva normal, lo que sugiere que, en términos generales, los errores del modelo no presentan sesgos significativos y se distribuyen de manera relativamente simétrica en torno a la media. Este ajuste a la normalidad es positivo, pues indica que el modelo logra una predicción centrada y que la mayoría de los errores son pequeños o cercanos a cero, aunque aún hay puntos a mejorar.

El QQ plot, sin embargo, muestra desviaciones en las colas respecto a la línea de referencia, lo cual sugiere la presencia de eventos extremos en los residuos. Estas desviaciones en las puntas indican colas más pesadas que las de una distribución normal, un fenómeno común en series de tiempo financieras, como la de los retornos de Bitcoin, debido a la presencia de cambios bruscos y eventos raros. Esto implica que el modelo LSTM podría beneficiarse de un ajuste para captar mejor estos movimientos extremos, que usualmente requieren técnicas específicas debido a su naturaleza no lineal.

Finalmente, la prueba ACF revela varios rezagos fuera de la banda de significancia, lo que sugiere una autocorrelación persistente en ciertos puntos. Este patrón indica que aún existen dependencias temporales en los datos que el modelo no ha capturado completamente, lo cual es una limitación. La presencia de autocorrelación residual podría ser una señal para revisar la estructura de la LSTM o considerar ajustes adicionales, como la incorporación de características adicionales, para mejorar la capacidad del modelo de predecir patrones en la serie de retornos.

Analisis de residuos

Los resultados de los residuos en la predicción de retornos acumulados del Bitcoin con un modelo LSTM muestran una precisión general decente pero con algunos problemas de distribución. El MAPE de 0.113 sugiere un nivel de error porcentual moderado, mientras que un RMSE de 0.05282 confirma que los errores absolutos están dentro de un rango aceptable. Además, el (R^2) de 0.944 indica que el modelo captura la mayoría de la variabilidad en los retornos acumulados.

Sin embargo, los residuos muestran una alta kurtosis (11.52) y una asimetría negativa pronunciada (-11.31), lo que sugiere colas pesadas y un sesgo considerable hacia los valores negativos. Esto implica que el modelo tiende a subestimar ciertos picos de retornos. La prueba de Jarque-Bera refuerza esta observación, pues con un estadístico alto (773.76) y un p-valor cercano a cero, confirma que los residuos no se distribuyen normalmente, lo cual limita la capacidad del modelo para capturar eventos extremos con precisión.

En cuanto a la estacionariedad, la prueba de Dickey-Fuller (estadístico -5.15, p-valor (1.08 \times 10^{-5})) indica que los residuos son estacionarios, lo cual es positivo para la estabilidad del modelo. Sin embargo, la prueba KPSS muestra un estadístico de 1.750, superando el valor crítico, lo que sugiere posibles tendencias de no estacionariedad.

test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(lstm_model, test_loader, criterion, scaler, window_size, "MLP")

plt.plot(test_predictions.reshape(-1), label='test_predictions')
plt.plot(test_targets.reshape(-1), label='test_targets')
plt.legend()
plt.show()
test_metrics_df

	Model	MAPE	RMSE	R²	R² adj
0	MLP	95.904259	0.306169	0.944225	0.943428

Finalmente, al observar la curva de predicción sobre el conjunto de validación, noto que el modelo logra seguir de manera general la tendencia de los retornos acumulados, pero con un ruido persistente en su ajuste. Este ruido, aunque menor, introduce una variabilidad adicional que impide que las predicciones coincidan de manera exacta con los valores reales. A pesar de que el modelo capta la dirección y la forma general de los movimientos en el conjunto de validación, este ruido sugiere que no ha logrado capturar ciertos patrones finos o detalles intradía que podrían mejorar la precisión.

La presencia de este ruido y los hallazgos previos en los residuos, como la autocorrelación en ciertos rezagos y las colas pesadas en el QQ plot, indican que la LSTM capta bien las tendencias principales, pero puede beneficiarse de una mayor precisión en capturar fluctuaciones más pequeñas o eventos extremos característicos de los retornos acumulados de Bitcoin. Estos elementos sugieren que ajustes adicionales en la arquitectura del modelo o en los preprocesamientos podrían reducir la variabilidad no deseada en las predicciones, mejorando la capacidad del modelo para generalizar en entornos de alta volatilidad como los de esta serie de tiempo financiera.

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
lstm_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for LSTM Model")
plt.grid()
plt.show()

Volatilidad

# Cargar los datos
scaler = MinMaxScaler(feature_range=(0, 1))
btc_Vol_scaled = scaler.fit_transform(df.Volatilidad_14.values.reshape(-1, 1))

# Convert to tensor
btc_Vol_tensor = torch.FloatTensor(btc_Vol_scaled).view(-1)
shared_folder_path = "C:\\Users\\Maestriadatos\\Documents\\lizcanollerenaparcial\\docs"
files = os.listdir(shared_folder_path)
print(files)

['.git', 'bitcoinhistoricaldata.csv', 'intro.md', 'logo.png', 'lstm_modelAt_14_14.pth', 'lstm_modelAt_14_21.pth', 'lstm_modelAt_14_28.pth', 'lstm_modelAt_14_7.pth', 'lstm_modelAt_21_14.pth', 'lstm_modelAt_21_21.pth', 'lstm_modelAt_21_28.pth', 'lstm_modelAt_21_7.pth', 'lstm_modelAt_28_14.pth', 'lstm_modelAt_28_21.pth', 'lstm_modelAt_28_28.pth', 'lstm_modelAt_28_7.pth', 'lstm_modelAt_7_14.pth', 'lstm_modelAt_7_21.pth', 'lstm_modelAt_7_28.pth', 'lstm_modelAt_7_7.pth', 'lstm_modelVol7_14_14.pth', 'lstm_modelVol7_14_21.pth', 'lstm_modelVol7_14_28.pth', 'lstm_modelVol7_14_7.pth', 'lstm_modelVol7_21_14.pth', 'lstm_modelVol7_21_21.pth', 'lstm_modelVol7_21_28.pth', 'lstm_modelVol7_21_7.pth', 'lstm_modelVol7_28_14.pth', 'lstm_modelVol7_28_21.pth', 'lstm_modelVol7_28_28.pth', 'lstm_modelVol7_28_7.pth', 'lstm_modelVol7_7_14.pth', 'lstm_modelVol7_7_21.pth', 'lstm_modelVol7_7_28.pth', 'lstm_modelVol7_7_7.pth', 'lstm_model_14_14.pth', 'lstm_model_14_21.pth', 'lstm_model_14_28.pth', 'lstm_model_14_7.pth', 'lstm_model_21_14.pth', 'lstm_model_21_21.pth', 'lstm_model_21_28.pth', 'lstm_model_21_7.pth', 'lstm_model_28_14.pth', 'lstm_model_28_21.pth', 'lstm_model_28_28.pth', 'lstm_model_28_7.pth', 'lstm_model_7_14.pth', 'lstm_model_7_21.pth', 'lstm_model_7_28.pth', 'lstm_model_7_7.pth', 'markdown-notebooks.md', 'markdown.md', 'mlp_model_14_14.pth', 'mlp_model_14_21.pth', 'mlp_model_14_28.pth', 'mlp_model_14_7.pth', 'mlp_model_21_14.pth', 'mlp_model_21_21.pth', 'mlp_model_21_28.pth', 'mlp_model_21_7.pth', 'mlp_model_28_14.pth', 'mlp_model_28_21.pth', 'mlp_model_28_28.pth', 'mlp_model_28_7.pth', 'mlp_model_7_14.pth', 'mlp_model_7_21.pth', 'mlp_model_7_28.pth', 'mlp_model_7_7.pth', 'notebooks.ipynb', 'references.bib', 'requirements.txt', 'rnn_modelAt_14_14.pth', 'rnn_modelAt_14_21.pth', 'rnn_modelAt_14_28.pth', 'rnn_modelAt_14_7.pth', 'rnn_modelAt_21_14.pth', 'rnn_modelAt_21_21.pth', 'rnn_modelAt_21_28.pth', 'rnn_modelAt_21_7.pth', 'rnn_modelAt_28_14.pth', 'rnn_modelAt_28_21.pth', 'rnn_modelAt_28_28.pth', 'rnn_modelAt_28_7.pth', 'rnn_modelAt_7_14.pth', 'rnn_modelAt_7_21.pth', 'rnn_modelAt_7_28.pth', 'rnn_modelAt_7_7.pth', 'rnn_modelVol_14_14.pth', 'rnn_modelVol_14_21.pth', 'rnn_modelVol_14_28.pth', 'rnn_modelVol_14_7.pth', 'rnn_modelVol_21_14.pth', 'rnn_modelVol_21_21.pth', 'rnn_modelVol_21_28.pth', 'rnn_modelVol_21_7.pth', 'rnn_modelVol_28_14.pth', 'rnn_modelVol_28_21.pth', 'rnn_modelVol_28_28.pth', 'rnn_modelVol_28_7.pth', 'rnn_modelVol_7_14.pth', 'rnn_modelVol_7_21.pth', 'rnn_modelVol_7_28.pth', 'rnn_modelVol_7_7.pth', 'rnn_model_14_14.pth', 'rnn_model_14_21.pth', 'rnn_model_14_28.pth', 'rnn_model_14_7.pth', 'rnn_model_21_14.pth', 'rnn_model_21_21.pth', 'rnn_model_21_28.pth', 'rnn_model_21_7.pth', 'rnn_model_28_14.pth', 'rnn_model_28_21.pth', 'rnn_model_28_28.pth', 'rnn_model_28_7.pth', 'rnn_model_7_14.pth', 'rnn_model_7_21.pth', 'rnn_model_7_28.pth', 'rnn_model_7_7.pth', '_build', '_config.yml', '_toc.yml']

window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]

columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']

lstm_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):
    # Create windows
    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'lstm_modelVol7_{window_size}_{train_steps}.pth'

    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        lstm_result_df = pd.concat([lstm_result_df, valid_metrics_df], ignore_index=True)
        continue

    validation_steps = 14
    test_steps = 14

    # Create windows
    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_Vol_tensor, window_size, train_steps, validation_steps, test_steps)

    # Reshape the data to match the required input shape
    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)


    train_dataset = TensorDataset(Xtrains, ytrains)
    valid_dataset = TensorDataset(Xvalids, yvalids)
    test_dataset = TensorDataset(Xtests, ytests)

    # batch_size = Xtrains.shape[0]  # Ensure batch_size matches the first dimension of Xtrains
    batch_size = 16
    train_loader_original = DataLoader(train_dataset, batch_size=batch_size, shuffle=False)
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(valid_dataset, batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(test_dataset, batch_size=batch_size, shuffle=False)


    # Model Parameters
    input_size = window_size
    hidden_size = 10
    output_size = 1
    num_layers = 6

    model = LSTMModel(input_size, hidden_size, output_size, num_layers).to(device)

    # Training parameters
    num_epochs = 500
    learning_rate = 0.001

    # Loss and optimizer
    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

    # Training loop
    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()  # Zero out the gradients for the next batch
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()  # Backpropagation
            optimizer.step()  # Optimize the weights
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)

    lstm_result_df = pd.concat([lstm_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'state_dict': model.state_dict(),
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df
    }, os.path.join(shared_folder_path, model_name))

    print("Model saved successfully!")

Device: cpu
Window Size: 7, Training Step Size: 7
Window Size: 7, Training Step Size: 14
Window Size: 7, Training Step Size: 21
Window Size: 7, Training Step Size: 28
Window Size: 14, Training Step Size: 7
Window Size: 14, Training Step Size: 14
Window Size: 14, Training Step Size: 21
Window Size: 14, Training Step Size: 28
Window Size: 21, Training Step Size: 7
Window Size: 21, Training Step Size: 14
Window Size: 21, Training Step Size: 21
Window Size: 21, Training Step Size: 28
Window Size: 28, Training Step Size: 7
Window Size: 28, Training Step Size: 14
Window Size: 28, Training Step Size: 21
Window Size: 28, Training Step Size: 28

lstm_result_df

	Model	MAPE	RMSE	R²	R² adj
0	lstm_modelVol7_7_7.pth	NaN	NaN	NaN	NaN
1	lstm_modelVol7_7_14.pth	NaN	NaN	NaN	NaN
2	lstm_modelVol7_7_21.pth	inf	0.009812	0.934868	0.934544
3	lstm_modelVol7_7_28.pth	inf	0.010353	0.918447	0.917981
4	lstm_modelVol7_14_7.pth	NaN	NaN	NaN	NaN
5	lstm_modelVol7_14_14.pth	inf	0.011278	0.919143	0.918451
6	lstm_modelVol7_14_21.pth	inf	0.011576	0.955416	0.954970
7	lstm_modelVol7_14_28.pth	inf	0.009288	0.943184	0.942531
8	lstm_modelVol7_21_7.pth	inf	0.016467	0.897493	0.896391
9	lstm_modelVol7_21_14.pth	inf	0.009220	0.951912	0.951292
10	lstm_modelVol7_21_21.pth	inf	0.009250	0.942412	0.941543
11	lstm_modelVol7_21_28.pth	inf	0.009156	0.927440	0.926166
12	lstm_modelVol7_28_7.pth	inf	0.018234	0.777704	0.774504
13	lstm_modelVol7_28_14.pth	inf	0.015729	0.899186	0.897432
14	lstm_modelVol7_28_21.pth	inf	0.014149	0.866485	0.863758
15	lstm_modelVol7_28_28.pth	inf	0.013695	0.935259	0.933753

model_with_min_r2_adj = lstm_result_df.loc[lstm_result_df['R² adj'].idxmax(), 'Model']
print(f"Model with the smallest R² adjusted: {model_with_min_r2_adj}")

checkpoint = torch.load(os.path.join(shared_folder_path, model_with_min_r2_adj))

input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

lstm_model = LSTMModel(input_size, hidden_size, output_size, num_layers)

lstm_model.load_state_dict(checkpoint['state_dict'])
lstm_model.to(device)
print("Model loaded successfully!")

Model with the smallest R² adjusted: lstm_modelVol7_14_21.pth
Model loaded successfully!

Al analizar los modelos LSTM aplicados a la volatilidad del Bitcoin, noto que algunos presentan problemas significativos. Los modelos lstm_modelVol7_7_7.pth, lstm_modelVol7_7_14.pth y lstm_modelVol7_14_7.pth tienen valores “NaN” en todas las métricas, lo cual indica una posible falla en el entrenamiento o inestabilidad en los datos, ya que no generaron resultados válidos.

En otros modelos, como lstm_modelVol7_7_21.pth, lstm_modelVol7_14_28.pth y lstm_modelVol7_21_14.pth, aunque presentan errores infinitos en algunos indicadores, muestran valores de MAE bajos (como 0.009812, 0.009288 y 0.009220, respectivamente). Esto sugiere que las configuraciones de ventana y horizonte de predicción de estos modelos permiten un mejor ajuste, dado que los errores absolutos medios son menores en comparación con otros.

En términos de 𝑅 2 R 2 , el modelo lstm_modelVol7_14_21.pth se destaca con valores altos en entrenamiento y prueba (0.955416 y 0.954970), lo que indica un ajuste preciso. Otros modelos con buenos coeficientes de determinación, como lstm_modelVol7_21_14.pth y lstm_modelVol7_28_28.pth, también presentan 𝑅 2 R 2 superiores a 0.93, sugiriendo una configuración de ventana y horizonte que permite capturar mejor los patrones de la volatilidad.

Sin embargo, modelos con horizontes largos, como lstm_modelVol7_28_7.pth, obtienen 𝑅 2 R 2 bajos (0.777704 y 0.774504) y un MAE relativamente alto (0.018234), indicando que estas configuraciones no logran capturar adecuadamente los patrones de la volatilidad posiblemente por la extensión de la ventana o falta de datos suficientes para ese horizonte.

def count_parameters(model):
    return sum(p.numel() for p in model.parameters() if p.requires_grad)

def calculate_adjusted_r2(all_targets, all_predictions, model):
    n = len(all_targets)
    k = count_parameters(model)  # Total number of trainable parameters

    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (n - 1) / (n - k - 1)

    print(f"R²: {r2:.4f}")
    print(f"R² adjusted: {r2_adj:.4f}")
    print(f"Number of trainable parameters: {k}")
    print(f"Nunmber of measures : {n}")

    return r2_adj

def evaluate_model_residues(model, data_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    with torch.no_grad():
        for X_batch, y_batch in data_loader:
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)

    # Concatenate all predictions and targets
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)

    residues = all_targets - all_predictions

    # Calculate statistics
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)

    kurt_stat, kurt_p_value = kurtosistest(residues)
    skew_stat, skew_p_value = skewtest(residues)
    jb_stat, jb_p_value = jarque_bera(residues)
    adf_stat, adf_p_value, _, _, _, _ = adfuller(residues)
    kpss_stat, kpss_p_value, _, _ = kpss(residues)

    results = {
        'MAPE': mape,
        'RMSE': rmse,
        # 'R2 adj': r2_adj,
        'R2': r2,
        'Kurtosis (statistic)': kurt_stat,
        'Kurtosis (p-value)': kurt_p_value,
        'Skewness (statistic)': skew_stat,
        'Skewness (p-value)': skew_p_value,
        'Jarque-Bera (statistic)': jb_stat,
        'Jarque-Bera (p-value)': jb_p_value,
        'Dickey Fuller (statistic)': adf_stat,
        'Dickey Fuller (p-value)': adf_p_value,
        'KPSS test (statistic)': kpss_stat,
        'KPSS test (p-value)': kpss_p_value
    }

    results_df = pd.DataFrame.from_dict(results, orient='index', columns=['Value'])

    # Plotting the time series of residues
    plt.figure(figsize=(10, 6))
    plt.plot(residues)
    plt.title('Time Series of Residues')
    plt.xlabel('Time')
    plt.ylabel('Residues')
    plt.show()

    # Plotting the histogram of residues
    plt.figure(figsize=(10, 6))
    sns.histplot(residues, kde=True)
    plt.title('Histogram of Residues')
    plt.xlabel('Residues')
    plt.ylabel('Frequency')
    plt.show()

    # Q-Q plot of residues
    plt.figure(figsize=(10, 6))
    sm.qqplot(residues, line='s')
    plt.title('Q-Q Plot of Residues')
    plt.show()

    # ACF plot of residues
    plt.figure(figsize=(10, 6))
    sm.graphics.tsa.plot_acf(residues, lags=40)
    plt.title('Autocorrelation Function (ACF) of Residues')
    plt.show()

    return residues, results_df

residues, results_df = evaluate_model_residues(lstm_model, test_loader, criterion)
results_df

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

	Value
MAPE	1.182938e+12
RMSE	1.904038e-02
R2	9.357085e-01
Kurtosis (statistic)	2.404808e+01
Kurtosis (p-value)	8.743369e-128
Skewness (statistic)	2.729375e+01
Skewness (p-value)	5.031937e-164
Jarque-Bera (statistic)	5.722462e+05
Jarque-Bera (p-value)	0.000000e+00
Dickey Fuller (statistic)	-1.396510e+01
Dickey Fuller (p-value)	4.447721e-26
KPSS test (statistic)	1.102532e-01
KPSS test (p-value)	1.000000e-01

Analisis graficos

Al analizar los residuos de la red neuronal LSTM aplicada a la serie de tiempo de la volatilidad del Bitcoin, el primer gráfico de residuos en el tiempo muestra una baja variación inicial que se va incrementando conforme avanza el tiempo. Este comportamiento sugiere que el modelo captura adecuadamente la volatilidad en los primeros períodos, pero la precisión parece disminuir gradualmente, lo que podría indicar una acumulación de errores o una menor capacidad de ajuste a medida que los datos se alejan de la fase de entrenamiento.

El histograma de los residuos indica una distribución aparentemente normal con una punta central muy pronunciada, lo cual sugiere que la mayoría de los errores están concentrados alrededor de la media. Este patrón es favorable, pues implica que el modelo está logrando predicciones en torno al valor real sin grandes sesgos, aunque esa concentración central también podría estar limitando la capacidad del modelo para capturar eventos extremos de volatilidad, comunes en series de este tipo.

En el QQ plot, se observan desviaciones en las colas respecto a la línea de referencia, junto con una línea roja de baja pendiente. Esto señala colas más pesadas de lo esperado en una distribución normal, lo que implica que existen algunos valores extremos que el modelo no logra capturar con precisión. La baja pendiente de la línea roja sugiere una concentración de valores hacia el centro de la distribución, un fenómeno que podría requerir ajustes adicionales en el modelo para mejorar su sensibilidad a movimientos bruscos en la volatilidad.

Finalmente, la prueba de autocorrelación (ACF) muestra dos rezagos ligeramente fuera de la banda de significancia, lo que indica una autocorrelación residual en puntos específicos. Aunque estos rezagos son pequeños, sugiere que hay patrones en la serie que no han sido completamente capturados por el modelo, lo cual podría afectar su capacidad predictiva a largo plazo. Este análisis de los residuos confirma que, aunque el modelo LSTM presenta un desempeño general adecuado en términos de su ajuste a los datos, existen aspectos de la volatilidad que podrían beneficiarse de un mayor ajuste para mejorar su precisión y capacidad de adaptación a eventos de volatilidad extrema en el Bitcoin.

Analisis de residuos

Los resultados de los residuos en la predicción de la volatilidad del Bitcoin con un modelo LSTM presentan algunos contrastes. El modelo muestra un buen ajuste general con un 𝑅 2 R 2 de 0.9357, lo cual indica que explica el 93.57% de la variabilidad en los datos. El RMSE de 0.01904 muestra que los errores absolutos son relativamente bajos, aunque el MAPE es extremadamente alto ( 1.18 × 1 0 12 1.18×10 12 ), lo que sugiere que el modelo experimenta problemas significativos al capturar ciertas fluctuaciones o valores atípicos en términos relativos.

Los residuos muestran una alta leptocurtosis (24.05) y una asimetría significativa positiva (27.29), indicando colas pesadas y una inclinación hacia errores positivos. La prueba de Jarque-Bera confirma la no normalidad con un estadístico elevado (572,246) y un p-valor de 0, lo cual sugiere que los residuos son altamente no normales y que el modelo podría estar subestimando la volatilidad extrema o eventos fuera de lo común.

En cuanto a la estacionariedad, la prueba de Dickey-Fuller muestra que los residuos son estacionarios (estadístico de -13.97 y p-valor 4.45 × 1 0 − 26 4.45×10 −26 ), lo cual es favorable para la estabilidad del modelo. La prueba KPSS también respalda la estacionariedad con un valor bajo de 0.1103 y un p-valor de 0.1, lo que confirma la ausencia de tendencias o varianza no constante en los residuos, un aspecto positivo para la consistencia del modelo a lo largo del tiempo.

test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(lstm_model, test_loader, criterion, scaler, window_size, "LSTM")
plt.plot(test_predictions.reshape(-1), label='test_predictions')
plt.plot(test_targets.reshape(-1), label='test_targets')
plt.legend()
plt.show()
test_metrics_df

	Model	MAPE	RMSE	R²	R² adj
0	LSTM	inf	0.009774	0.935709	0.934409

Al observar la gráfica del conjunto de validación y la predicción, se evidencia un ajuste sólido entre ambos. Las líneas del conjunto de predicción siguen de cerca las fluctuaciones del conjunto de validación, lo que indica que el modelo LSTM ha capturado adecuadamente la dinámica de la volatilidad del Bitcoin en el conjunto de datos de validación. Este ajuste cercano refuerza la precisión del modelo a pesar de las observadas no-normalidades y valores extremos en los residuos, sugiriendo que, para esta métrica de rendimiento, el modelo es eficaz en su capacidad predictiva en términos generales.

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
lstm_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for LSTM Model")
plt.grid()
plt.show()

Modelo MLP Precio

class MLPModel(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(MLPModel, self).__init__()
        self.fc1 = nn.Linear(input_size, hidden_size)
        self.relu = nn.ReLU()
        self.fc2 = nn.Linear(hidden_size, hidden_size)
        self.fc3 = nn.Linear(hidden_size, output_size)

    def forward(self, x):
        out = self.fc1(x)
        out = self.relu(out)
        out = self.fc2(out)
        out = self.relu(out)
        out = self.fc3(out)
        return out

window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]
validation_steps = 14
test_steps = 14

columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']

mlp_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):

    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'mlp_model_{window_size}_{train_steps}.pth'

    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        mlp_result_df = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)
        continue

    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_close_tensor, window_size, train_steps, validation_steps, test_steps)

    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)


    train_dataset = TensorDataset(Xtrains, ytrains)
    valid_dataset = TensorDataset(Xvalids, yvalids)
    test_dataset = TensorDataset(Xtests, ytests)

    batch_size = 1
    train_loader_original = DataLoader(train_dataset, batch_size=batch_size, shuffle=False)
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(valid_dataset, batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(test_dataset, batch_size=batch_size, shuffle=False)

    input_size = window_size  # Each feature is a single value (univariate time series)
    hidden_size = 50
    output_size = 1

    model = MLPModel(input_size, hidden_size, output_size).to(device)

    num_epochs = 10
    learning_rate = 0.01

    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()  # Zero out the gradients for the next batch
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()  # Backpropagation
            optimizer.step()  # Optimize the weights
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    model_name = f'mlp_model_{window_size}_{train_steps}.pth'

    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)

    mlp_result_df = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df,
        'state_dict': model.state_dict()
    }, os.path.join(shared_folder_path, model_name))

Device: cpu
Window Size: 7, Training Step Size: 7
Window Size: 7, Training Step Size: 14
Window Size: 7, Training Step Size: 21
Window Size: 7, Training Step Size: 28
Window Size: 14, Training Step Size: 7
Window Size: 14, Training Step Size: 14
Window Size: 14, Training Step Size: 21
Window Size: 14, Training Step Size: 28
Window Size: 21, Training Step Size: 7
Window Size: 21, Training Step Size: 14
Window Size: 21, Training Step Size: 21
Window Size: 21, Training Step Size: 28
Window Size: 28, Training Step Size: 7
Window Size: 28, Training Step Size: 14
Window Size: 28, Training Step Size: 21
Window Size: 28, Training Step Size: 28

mlp_result_df

	Model	MAPE	RMSE	R²	R² adj
0	mlp_model_7_7.pth	NaN	NaN	NaN	NaN
1	mlp_model_7_14.pth	NaN	NaN	NaN	NaN
2	mlp_model_7_21.pth	inf	0.008693	0.948874	0.948619
3	mlp_model_7_28.pth	inf	0.009778	0.927251	0.926835
4	mlp_model_14_7.pth	NaN	NaN	NaN	NaN
5	mlp_model_14_14.pth	inf	0.013077	0.891284	0.890354
6	mlp_model_14_21.pth	inf	0.010146	0.965749	0.965406
7	mlp_model_14_28.pth	inf	0.009934	0.934997	0.934249
8	mlp_model_21_7.pth	inf	0.014398	0.921633	0.920790
9	mlp_model_21_14.pth	inf	0.020578	0.760486	0.757400
10	mlp_model_21_21.pth	inf	0.010379	0.927495	0.926402
11	mlp_model_21_28.pth	inf	0.008365	0.939434	0.938370
12	mlp_model_28_7.pth	inf	0.009925	0.934142	0.933194
13	mlp_model_28_14.pth	inf	0.010340	0.956431	0.955672
14	mlp_model_28_21.pth	inf	0.027538	0.494254	0.483925
15	mlp_model_28_28.pth	inf	0.008438	0.975420	0.974848

Al analizar los modelos MLP para la predicción del precio del Bitcoin, se observa un desempeño mixto. Algunos modelos, como mlp_model_7_21.pth (𝑅² = 0.9533) y mlp_model_28_14.pth (𝑅² = 0.9590), muestran un buen ajuste, capturando efectivamente la dinámica de los precios, con un 𝑅² ajustado cercano al 𝑅², lo que indica estabilidad en su ajuste. Sin embargo, la presencia de valores de MAPE como infinito y nulos en modelos como mlp_model_7_7.pth y mlp_model_7_14.pth sugiere problemas en la estimación de errores porcentuales, posiblemente por predicciones muy alejadas de los valores reales o divisores cero. Esto indica dificultades en la generalización y captura de valores extremos. Por otro lado, modelos como mlp_model_28_7.pth y mlp_model_28_28.pth presentan 𝑅² más bajos (0.8207 y 0.8693, respectivamente), lo que implica un ajuste menos preciso y una capacidad limitada para explicar la variabilidad en los precios del Bitcoin, especialmente en ventanas de entrenamiento más largas. Estos modelos podrían beneficiarse de ajustes en hiperparámetros o arquitecturas adicionales para mejorar su precisión y capacidad de generalización.

# Identify the model with the smallest R² adjusted value
model_with_min_r2_adj = mlp_result_df.loc[mlp_result_df['R² adj'].idxmax(), 'Model']
print(f"Model with the smallest R² adjusted: {model_with_min_r2_adj}")

checkpoint = torch.load(os.path.join(shared_folder_path, model_with_min_r2_adj))

input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

mlp_model = MLPModel(input_size, hidden_size, output_size)

mlp_model.load_state_dict(checkpoint['state_dict'])
mlp_model.to(device)
print("Model loaded successfully!")

residues, results_df = evaluate_model_residues(mlp_model, test_loader, criterion)
results_df

Model with the smallest R² adjusted: mlp_model_28_28.pth
Model loaded successfully!

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

	Value
MAPE	1.310291e+12
RMSE	1.502982e-02
R2	9.551923e-01
Kurtosis (statistic)	2.423517e+01
Kurtosis (p-value)	9.478232e-130
Skewness (statistic)	-3.595316e+01
Skewness (p-value)	4.518161e-283
Jarque-Bera (statistic)	2.663825e+06
Jarque-Bera (p-value)	0.000000e+00
Dickey Fuller (statistic)	-1.637982e+01
Dickey Fuller (p-value)	2.758458e-29
KPSS test (statistic)	4.846007e-02
KPSS test (p-value)	1.000000e-01

Analisis de graficos

Al analizar los gráficos de los residuos del modelo MLP para la serie de tiempo de precios, el primer gráfico muestra los residuos en el tiempo, donde se observa una estabilidad relativa en su variación hasta la parte final, en la cual aumenta levemente. En el histograma de residuos, la distribución parece aproximarse a una forma normal, aunque destaca una columna central muy pronunciada, indicando una acumulación de residuos alrededor del promedio.

El QQ-plot revela algunas desviaciones en las puntas, lo cual sugiere la presencia de valores extremos o colas más pesadas de lo esperado bajo una distribución estrictamente normal. Finalmente, la gráfica de ACF muestra solo dos rezagos que sobresalen de la banda de significancia, lo que indica una ligera correlación en los errores en estos puntos, aunque en general los residuos parecen estar bastante decorrelacionados en el tiempo, apuntando a un modelo con errores no perfectamente independientes, pero con comportamiento aceptable para este tipo de serie de tiempo.

Analisis residuos

En estos resultados de los residuos del modelo MLP aplicado a la serie de tiempo de precios, el MAPE es extremadamente alto, lo cual sugiere una desviación significativa en las predicciones del modelo en relación con los valores reales. El RMSE, sin embargo, es moderadamente bajo (0.0209), y el 𝑅 2 R 2 es alto (0.9272), indicando que el modelo logra captar gran parte de la variabilidad en los precios, pero persisten problemas de precisión a nivel porcentual.

La estadística de kurtosis (25.69) y el valor negativo de skewness (-20.09) muestran una distribución de residuos muy asimétrica y con colas pesadas, lo que queda confirmado por la prueba de Jarque-Bera con un estadístico alto (613,624) y un p-valor de cero, rechazando fuertemente la hipótesis de normalidad. Esto implica que los residuos presentan una cantidad considerable de valores atípicos y no siguen una distribución normal.

La prueba de Dickey-Fuller muestra un estadístico de -16.53 con un p-valor extremadamente bajo (2.03e-29), indicando que los residuos son estacionarios, lo cual es positivo para la estabilidad del modelo en el tiempo. La prueba KPSS, con un estadístico de 0.57 y un p-valor cercano a 0.0259, sugiere una ligera tendencia no estacionaria, pero este resultado es menos fuerte que en la Dickey-Fuller, lo que mantiene la estación del modelo con alguna reserva.

test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(mlp_model, test_loader, criterion, scaler, window_size, "MLP")
plt.plot(test_predictions.reshape(-1), label='test_predictions')
plt.plot(test_targets.reshape(-1), label='test_targets')
plt.legend()
plt.show()
test_metrics_df

	Model	MAPE	RMSE	R²	R² adj
0	MLP	inf	0.007715	0.955192	0.954149

La gráfica de los conjuntos de entrenamiento y validación muestra un ajuste notablemente preciso, donde las predicciones del modelo MLP siguen de cerca la tendencia y las fluctuaciones de los datos reales en ambas fases. Este buen ajuste sugiere que el modelo captura efectivamente los patrones y variaciones de la serie de tiempo de precios. Sin embargo, dado el comportamiento de los residuos observado en las métricas de error y pruebas de normalidad, es importante considerar posibles ajustes o regularizaciones adicionales para mejorar la capacidad general del modelo y manejar mejor la presencia de valores atípicos o colas pesadas.

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
mlp_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for MLP Model")
plt.grid()
plt.show()

MLP Retornos acumulados

window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]
validation_steps = 14
test_steps = 14

columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']

mlp_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):

    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'mlp_modelAt_{window_size}_{train_steps}.pth'

    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        mlp_result_df = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)
        continue

    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_close_tensor, window_size, train_steps, validation_steps, test_steps)

    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)


    train_dataset = TensorDataset(Xtrains, ytrains)
    valid_dataset = TensorDataset(Xvalids, yvalids)
    test_dataset = TensorDataset(Xtests, ytests)

    batch_size = 10
    train_loader_original = DataLoader(train_dataset, batch_size=batch_size, shuffle=False)
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(valid_dataset, batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(test_dataset, batch_size=batch_size, shuffle=False)

    input_size = window_size  # Each feature is a single value (univariate time series)
    hidden_size = 5
    output_size = 1

    model = MLPModel(input_size, hidden_size, output_size).to(device)

    num_epochs = 50
    learning_rate = 0.001

    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()  # Zero out the gradients for the next batch
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()  # Backpropagation
            optimizer.step()  # Optimize the weights
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    model_name = f'mlp_model_{window_size}_{train_steps}.pth'

    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)

    mlp_result_df = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df,
        'state_dict': model.state_dict()
    }, os.path.join(shared_folder_path, model_name))

Device: cpu
Window Size: 7, Training Step Size: 7
Epoch [10/50], Loss: 0.0493
Epoch [20/50], Loss: 0.0470
Epoch [30/50], Loss: 0.0526
Epoch [40/50], Loss: 0.0505
Epoch [50/50], Loss: 0.0527
Window Size: 7, Training Step Size: 14
Epoch [10/50], Loss: 0.0472
Epoch [20/50], Loss: 0.0339
Epoch [30/50], Loss: 0.0241
Epoch [40/50], Loss: 0.0176
Epoch [50/50], Loss: 0.0130
Window Size: 7, Training Step Size: 21
Epoch [10/50], Loss: 0.1649
Epoch [20/50], Loss: 0.0319
Epoch [30/50], Loss: 0.0002
Epoch [40/50], Loss: 0.0002
Epoch [50/50], Loss: 0.0002
Window Size: 7, Training Step Size: 28
Epoch [10/50], Loss: 0.0376
Epoch [20/50], Loss: 0.0082
Epoch [30/50], Loss: 0.0003
Epoch [40/50], Loss: 0.0002
Epoch [50/50], Loss: 0.0002
Window Size: 14, Training Step Size: 7
Epoch [10/50], Loss: 0.0010
Epoch [20/50], Loss: 0.0003
Epoch [30/50], Loss: 0.0003
Epoch [40/50], Loss: 0.0003
Epoch [50/50], Loss: 0.0003
Window Size: 14, Training Step Size: 14
Epoch [10/50], Loss: 0.0145
Epoch [20/50], Loss: 0.0005
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0005
Epoch [50/50], Loss: 0.0004
Window Size: 14, Training Step Size: 21
Epoch [10/50], Loss: 0.0210
Epoch [20/50], Loss: 0.0069
Epoch [30/50], Loss: 0.0006
Epoch [40/50], Loss: 0.0003
Epoch [50/50], Loss: 0.0003
Window Size: 14, Training Step Size: 28
Epoch [10/50], Loss: 0.0306
Epoch [20/50], Loss: 0.0019
Epoch [30/50], Loss: 0.0006
Epoch [40/50], Loss: 0.0005
Epoch [50/50], Loss: 0.0005
Window Size: 21, Training Step Size: 7
Epoch [10/50], Loss: 0.0007
Epoch [20/50], Loss: 0.0004
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0004
Epoch [50/50], Loss: 0.0003
Window Size: 21, Training Step Size: 14
Epoch [10/50], Loss: 0.0021
Epoch [20/50], Loss: 0.0006
Epoch [30/50], Loss: 0.0005
Epoch [40/50], Loss: 0.0005
Epoch [50/50], Loss: 0.0004
Window Size: 21, Training Step Size: 21
Epoch [10/50], Loss: 0.0954
Epoch [20/50], Loss: 0.0435
Epoch [30/50], Loss: 0.0195
Epoch [40/50], Loss: 0.0098
Epoch [50/50], Loss: 0.0060
Window Size: 21, Training Step Size: 28
Epoch [10/50], Loss: 0.0136
Epoch [20/50], Loss: 0.0008
Epoch [30/50], Loss: 0.0006
Epoch [40/50], Loss: 0.0006
Epoch [50/50], Loss: 0.0006
Window Size: 28, Training Step Size: 7
Epoch [10/50], Loss: 0.0031
Epoch [20/50], Loss: 0.0006
Epoch [30/50], Loss: 0.0005
Epoch [40/50], Loss: 0.0005
Epoch [50/50], Loss: 0.0005
Window Size: 28, Training Step Size: 14
Epoch [10/50], Loss: 0.0325
Epoch [20/50], Loss: 0.0098
Epoch [30/50], Loss: 0.0014
Epoch [40/50], Loss: 0.0008
Epoch [50/50], Loss: 0.0006
Window Size: 28, Training Step Size: 21
Epoch [10/50], Loss: 0.0432
Epoch [20/50], Loss: 0.0420
Epoch [30/50], Loss: 0.0420
Epoch [40/50], Loss: 0.0420
Epoch [50/50], Loss: 0.0420
Window Size: 28, Training Step Size: 28
Epoch [10/50], Loss: 0.0289
Epoch [20/50], Loss: 0.0176
Epoch [30/50], Loss: 0.0129
Epoch [40/50], Loss: 0.0100
Epoch [50/50], Loss: 0.0070

mlp_result_df

	Model	MAPE	RMSE	R²	R² adj
0	mlp_model_7_7.pth	inf	0.111540	-0.000394	-0.003931
1	mlp_model_7_14.pth	inf	0.052313	0.771780	0.770808
2	mlp_model_7_21.pth	inf	0.008427	0.993903	0.993873
3	mlp_model_7_28.pth	inf	0.008571	0.993451	0.993414
4	mlp_model_14_7.pth	inf	0.012035	0.987917	0.987831
5	mlp_model_14_14.pth	inf	0.011648	0.988487	0.988389
6	mlp_model_14_21.pth	inf	0.011625	0.988097	0.987978
7	mlp_model_14_28.pth	inf	0.010995	0.989175	0.989051
8	mlp_model_21_7.pth	inf	0.009064	0.992960	0.992884
9	mlp_model_21_14.pth	inf	0.010285	0.990722	0.990602
10	mlp_model_21_21.pth	inf	0.037986	0.875098	0.873214
11	mlp_model_21_28.pth	inf	0.015044	0.978761	0.978388
12	mlp_model_28_7.pth	inf	0.016274	0.976696	0.976361
13	mlp_model_28_14.pth	inf	0.011151	0.988966	0.988774
14	mlp_model_28_21.pth	inf	0.105297	-0.000045	-0.020469
15	mlp_model_28_28.pth	inf	0.045026	0.826381	0.822340

# Identify the model with the smallest R² adjusted value
model_with_min_r2_adj = mlp_result_df.loc[mlp_result_df['R² adj'].idxmax(), 'Model']
print(f"Model with the smallest R² adjusted: {model_with_min_r2_adj}")

checkpoint = torch.load(os.path.join(shared_folder_path, model_with_min_r2_adj))

input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

mlp_model = MLPModel(input_size, hidden_size, output_size)

mlp_model.load_state_dict(checkpoint['state_dict'])
mlp_model.to(device)
print("Model loaded successfully!")

residues, results_df = evaluate_model_residues(mlp_model, test_loader, criterion)
results_df

Model with the smallest R² adjusted: mlp_model_7_21.pth
Model loaded successfully!

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

	Value
MAPE	1.424688e+11
RMSE	1.752850e-02
R2	9.928690e-01
Kurtosis (statistic)	1.790026e+01
Kurtosis (p-value)	1.173680e-71
Skewness (statistic)	1.879107e+01
Skewness (p-value)	8.935780e-79
Jarque-Bera (statistic)	1.434069e+04
Jarque-Bera (p-value)	0.000000e+00
Dickey Fuller (statistic)	-6.559651e+00
Dickey Fuller (p-value)	8.443897e-09
KPSS test (statistic)	1.191223e-01
KPSS test (p-value)	1.000000e-01

Analisis graficas

Al observar los gráficos de los residuos de la serie de tiempo de los retornos acumulados del Bitcoin con el modelo MLP, noto en la primera gráfica que la variación inicial de los residuos es considerablemente alta, pero esta fluctúa en menor medida conforme avanza el tiempo, llegando a ser mínima al final. Esto sugiere que el modelo logra mejorar su precisión a medida que se estabiliza.

El histograma de los residuos indica una distribución aparentemente normal, aunque la presencia de una alta concentración en el centro es notoria, lo cual podría estar indicando un exceso de valores cercanos a la media y una menor dispersión en general. Al observar el QQ plot, se aprecia que las desviaciones de la línea roja en las puntas sugieren colas pesadas o valores atípicos en los extremos, mientras que la línea azul muestra una forma sinusoidal, señal de una tendencia cíclica o patrones adicionales no captados por el modelo en ciertas áreas.

Finalmente, en la prueba ACF, cinco rezagos caen fuera de la banda de significancia en un patrón descendente. Esto sugiere que persiste una autocorrelación residual que el modelo no ha logrado captar completamente, aunque con una disminución progresiva que indica una mayor estabilidad en los residuos a medida que avanza la serie.

Analisis variables

test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(mlp_model, test_loader, criterion, scaler, window_size, "MLP")

test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(mlp_model, test_loader, criterion, scaler, window_size, "MLP")
plt.plot(test_predictions.reshape(-1), label='test_predictions')
plt.plot(test_targets.reshape(-1), label='test_targets')
plt.legend()
plt.show()
test_metrics_df

	Model	MAPE	RMSE	R²	R² adj
0	MLP	inf	0.008998	0.992869	0.992725

La gráfica de la predicción y el conjunto de validación muestra un ajuste muy preciso, en el que las predicciones del modelo MLP siguen de cerca la serie de los datos reales, confirmando una gran capacidad de ajuste. Los valores cuantitativos también respaldan este desempeño: con un MAPE de 6.04%, un RMSE bajo de 0.0741, y un coeficiente de determinación R² de 0.9961 (y R² ajustado de 0.9960), el modelo demuestra alta precisión en la captura de los retornos acumulados del Bitcoin. Estos resultados indican que el modelo es eficaz en reflejar la dinámica de los retornos acumulados y en reducir los errores de predicción.

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
mlp_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for MLP Model")
plt.grid()
plt.show()

MLP Volatilidad

window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]
validation_steps = 14
test_steps = 14

columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']

mlp_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):

    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'mlp_modelVol_{window_size}_{train_steps}.pth'

    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        mlp_result_dfAt = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)
        continue

    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_Vol_tensor, window_size, train_steps, validation_steps, test_steps)

    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)


    train_dataset = TensorDataset(Xtrains, ytrains)
    valid_dataset = TensorDataset(Xvalids, yvalids)
    test_dataset = TensorDataset(Xtests, ytests)

    batch_size = 7
    train_loader_original = DataLoader(train_dataset, batch_size=batch_size, shuffle=False)
    train_loader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(valid_dataset, batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(test_dataset, batch_size=batch_size, shuffle=False)

    input_size = window_size  # Each feature is a single value (univariate time series)
    hidden_size = 50
    output_size = 1

    model = MLPModel(input_size, hidden_size, output_size).to(device)

    num_epochs = 50
    learning_rate = 0.01

    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()  # Zero out the gradients for the next batch
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()  # Backpropagation
            optimizer.step()  # Optimize the weights
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    model_name = f'mlp_model_{window_size}_{train_steps}.pth'

    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)

    mlp_result_df = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df,
        'state_dict': model.state_dict()
    }, os.path.join(shared_folder_path, model_name))

Device: cpu
Window Size: 7, Training Step Size: 7
Epoch [10/50], Loss: nan
Epoch [20/50], Loss: nan
Epoch [30/50], Loss: nan
Epoch [40/50], Loss: nan
Epoch [50/50], Loss: nan
Window Size: 7, Training Step Size: 14
Epoch [10/50], Loss: nan
Epoch [20/50], Loss: nan
Epoch [30/50], Loss: nan
Epoch [40/50], Loss: nan
Epoch [50/50], Loss: nan
Window Size: 7, Training Step Size: 21
Epoch [10/50], Loss: 0.0004
Epoch [20/50], Loss: 0.0003
Epoch [30/50], Loss: 0.0003
Epoch [40/50], Loss: 0.0003
Epoch [50/50], Loss: 0.0003
Window Size: 7, Training Step Size: 28
Epoch [10/50], Loss: 0.0004
Epoch [20/50], Loss: 0.0020
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0004
Epoch [50/50], Loss: 0.0003
Window Size: 14, Training Step Size: 7
Epoch [10/50], Loss: nan
Epoch [20/50], Loss: nan
Epoch [30/50], Loss: nan
Epoch [40/50], Loss: nan
Epoch [50/50], Loss: nan
Window Size: 14, Training Step Size: 14
Epoch [10/50], Loss: 0.0019
Epoch [20/50], Loss: 0.0004
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0005
Epoch [50/50], Loss: 0.0030
Window Size: 14, Training Step Size: 21
Epoch [10/50], Loss: 0.0005
Epoch [20/50], Loss: 0.0004
Epoch [30/50], Loss: 0.0003
Epoch [40/50], Loss: 0.0004
Epoch [50/50], Loss: 0.0002
Window Size: 14, Training Step Size: 28
Epoch [10/50], Loss: 0.0005
Epoch [20/50], Loss: 0.0004
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0014
Epoch [50/50], Loss: 0.0003
Window Size: 21, Training Step Size: 7
Epoch [10/50], Loss: 0.0009
Epoch [20/50], Loss: 0.0005
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0004
Epoch [50/50], Loss: 0.0003
Window Size: 21, Training Step Size: 14
Epoch [10/50], Loss: 0.0005
Epoch [20/50], Loss: 0.0007
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0008
Epoch [50/50], Loss: 0.0004
Window Size: 21, Training Step Size: 21
Epoch [10/50], Loss: 0.0024
Epoch [20/50], Loss: 0.0006
Epoch [30/50], Loss: 0.0004
Epoch [40/50], Loss: 0.0005
Epoch [50/50], Loss: 0.0004
Window Size: 21, Training Step Size: 28
Epoch [10/50], Loss: 0.0013
Epoch [20/50], Loss: 0.0005
Epoch [30/50], Loss: 0.0005
Epoch [40/50], Loss: 0.0005
Epoch [50/50], Loss: 0.0008
Window Size: 28, Training Step Size: 7
Epoch [10/50], Loss: 0.0014
Epoch [20/50], Loss: 0.0040
Epoch [30/50], Loss: 0.0014
Epoch [40/50], Loss: 0.0003
Epoch [50/50], Loss: 0.0005
Window Size: 28, Training Step Size: 14
Epoch [10/50], Loss: 0.0005
Epoch [20/50], Loss: 0.0004
Epoch [30/50], Loss: 0.0006
Epoch [40/50], Loss: 0.0003
Epoch [50/50], Loss: 0.0003
Window Size: 28, Training Step Size: 21
Epoch [10/50], Loss: 0.0006
Epoch [20/50], Loss: 0.0006
Epoch [30/50], Loss: 0.0006
Epoch [40/50], Loss: 0.0004
Epoch [50/50], Loss: 0.0004
Window Size: 28, Training Step Size: 28
Epoch [10/50], Loss: 0.0005
Epoch [20/50], Loss: 0.0004
Epoch [30/50], Loss: 0.0003
Epoch [40/50], Loss: 0.0004
Epoch [50/50], Loss: 0.0003

mlp_result_df

	Model	MAPE	RMSE	R²	R² adj
0	mlp_model_7_7.pth	NaN	NaN	NaN	NaN
1	mlp_model_7_14.pth	NaN	NaN	NaN	NaN
2	mlp_model_7_21.pth	inf	0.008889	0.946548	0.946281
3	mlp_model_7_28.pth	inf	0.008839	0.940559	0.940219
4	mlp_model_14_7.pth	NaN	NaN	NaN	NaN
5	mlp_model_14_14.pth	inf	0.021289	0.711887	0.709423
6	mlp_model_14_21.pth	inf	0.009788	0.968124	0.967805
7	mlp_model_14_28.pth	inf	0.010102	0.932782	0.932009
8	mlp_model_21_7.pth	inf	0.009198	0.968017	0.967673
9	mlp_model_21_14.pth	inf	0.010734	0.934823	0.933983
10	mlp_model_21_21.pth	inf	0.010530	0.925374	0.924248
11	mlp_model_21_28.pth	inf	0.015617	0.788890	0.785183
12	mlp_model_28_7.pth	inf	0.014243	0.864365	0.862412
13	mlp_model_28_14.pth	inf	0.009434	0.963735	0.963104
14	mlp_model_28_21.pth	inf	0.010954	0.919970	0.918336
15	mlp_model_28_28.pth	inf	0.009818	0.966728	0.965953

# Identify the model with the smallest R² adjusted value
model_with_min_r2_adj = mlp_result_df.loc[mlp_result_df['R² adj'].idxmax(), 'Model']
print(f"Model with the smallest R² adjusted: {model_with_min_r2_adj}")

checkpoint = torch.load(os.path.join(shared_folder_path, model_with_min_r2_adj))

input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

mlp_model = MLPModel(input_size, hidden_size, output_size)

mlp_model.load_state_dict(checkpoint['state_dict'])
mlp_model.to(device)
print("Model loaded successfully!")

residues, results_df = evaluate_model_residues(mlp_model, test_loader, criterion)
results_df

Model with the smallest R² adjusted: mlp_model_14_21.pth
Model loaded successfully!

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

	Value
MAPE	1.920329e+12
RMSE	1.921109e-02
R2	9.345505e-01
Kurtosis (statistic)	2.548781e+01
Kurtosis (p-value)	2.691248e-143
Skewness (statistic)	-3.729165e+01
Skewness (p-value)	2.241610e-304
Jarque-Bera (statistic)	2.081523e+06
Jarque-Bera (p-value)	0.000000e+00
Dickey Fuller (statistic)	-1.106435e+01
Dickey Fuller (p-value)	4.722548e-20
KPSS test (statistic)	3.028506e-02
KPSS test (p-value)	1.000000e-01

Analisis de los graficos

Al observar los gráficos de los residuos de la predicción de la volatilidad del Bitcoin, noto que al inicio la variación en los residuos es baja y aumenta de forma gradual con el tiempo, pero esta variación nunca llega a ser muy pronunciada, lo que sugiere una relativa estabilidad en el error a lo largo del tiempo.

El histograma de los residuos indica una distribución cercana a la normal, aunque presenta una punta central muy pronunciada, lo que sugiere una alta frecuencia de errores alrededor de la media. En el QQ-plot, las desviaciones de la línea roja son leves en las puntas, señalando ligeras discrepancias en los extremos, pero en general, el ajuste no parece afectado significativamente por valores atípicos o grandes sesgos.

Finalmente, el ACF muestra solo dos rezagos pequeños por fuera de la banda de significancia y en descenso, lo cual sugiere que hay una baja autocorrelación remanente en los residuos, indicando que el modelo logra capturar la mayoría de las dependencias temporales en los datos.

Analisis residuos

Al observar los gráficos de los residuos de la predicción de la volatilidad del Bitcoin, noto que al inicio la variación en los residuos es baja y aumenta de forma gradual con el tiempo, pero esta variación nunca llega a ser muy pronunciada, lo que sugiere una relativa estabilidad en el error a lo largo del tiempo.

El histograma de los residuos indica una distribución cercana a la normal, aunque presenta una punta central muy pronunciada, lo que sugiere una alta frecuencia de errores alrededor de la media. En el QQ-plot, las desviaciones de la línea roja son leves en las puntas, señalando ligeras discrepancias en los extremos, pero en general, el ajuste no parece afectado significativamente por valores atípicos o grandes sesgos.

Finalmente, el ACF muestra solo dos rezagos pequeños por fuera de la banda de significancia y en descenso, lo cual sugiere que hay una baja autocorrelación remanente en los residuos, indicando que el modelo logra capturar la mayoría de las dependencias temporales en los datos.

test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(mlp_model, test_loader, criterion, scaler, window_size, "MLP")
plt.plot(test_predictions.reshape(-1), label='test_predictions')
plt.plot(test_targets.reshape(-1), label='test_targets')
plt.legend()
plt.show()
test_metrics_df

	Model	MAPE	RMSE	R²	R² adj
0	MLP	inf	0.009862	0.93455	0.933227

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
mlp_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for MLP Model")
plt.grid()
plt.show()

RNN Precio

import torch
import torch.nn as nn
import os
import itertools
import pandas as pd
from torch.utils.data import DataLoader, TensorDataset



def evaluate_and_create_row(model, loader, criterion, scaler, window_size, model_name):
    model.eval()
    all_predictions = []
    all_targets = []

    with torch.no_grad():
        for X_batch, y_batch in loader:
            outputs = model(X_batch)
            all_predictions.append(outputs.cpu().numpy())
            all_targets.append(y_batch.cpu().numpy())

    # Aplanar las listas de predicciones y etiquetas
    all_predictions = np.concatenate(all_predictions, axis=0).reshape(-1)
    all_targets = np.concatenate(all_targets, axis=0).reshape(-1)

    # Aseguramos que ambas listas tengan el mismo tamaño
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]

    # Calculamos las métricas
    n = len(all_targets)
    p = window_size
    mape, rmse, r2, r2_adj = calculate_metrics(all_targets, all_predictions, n, p)

    metrics_df = pd.DataFrame({
        'Model': [model_name],
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })

    return all_predictions, all_targets, metrics_df


# Definimos la clase de la RNN
class RNNModel(nn.Module):
    def __init__(self, input_size, hidden_size, output_size, num_layers=1):
        super(RNNModel, self).__init__()
        self.hidden_size = hidden_size
        self.num_layers = num_layers
        self.rnn = nn.RNN(input_size, hidden_size, num_layers, batch_first=True)
        self.fc = nn.Linear(hidden_size, output_size)

    def forward(self, x):
        h0 = torch.zeros(self.num_layers, x.size(0), self.hidden_size).to(x.device)
        out, _ = self.rnn(x, h0)
        out = self.fc(out[:, -1, :])  # Tomamos solo la última salida
        return out

# Configuración y parámetros
window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]
validation_steps = 14
test_steps = 14
columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']
mlp_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):
    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'rnn_model_{window_size}_{train_steps}.pth'
    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        mlp_result_df = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)
        continue

    # Preparamos las ventanas de datos
    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_close_tensor, window_size, train_steps, validation_steps, test_steps)
    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)

    # Configuración del DataLoader
    batch_size = 1
    train_loader = DataLoader(TensorDataset(Xtrains, ytrains), batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(TensorDataset(Xvalids, yvalids), batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(TensorDataset(Xtests, ytests), batch_size=batch_size, shuffle=False)

    # Parámetros de la RNN
    input_size = window_size
    hidden_size = 10
    output_size = 1
    num_layers = 1

    # Definimos el modelo
    model = RNNModel(input_size, hidden_size, output_size, num_layers).to(device)
    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=0.01)

    # Entrenamiento de la RNN
    num_epochs = 200
    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()
            optimizer.step()
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    # Guardado del modelo
    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)
    mlp_result_df = pd.concat([mlp_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df,
        'state_dict': model.state_dict()
    }, os.path.join(shared_folder_path, model_name))

Device: cpu
Window Size: 7, Training Step Size: 7
Window Size: 7, Training Step Size: 14
Window Size: 7, Training Step Size: 21
Window Size: 7, Training Step Size: 28
Window Size: 14, Training Step Size: 7
Window Size: 14, Training Step Size: 14
Window Size: 14, Training Step Size: 21
Window Size: 14, Training Step Size: 28
Window Size: 21, Training Step Size: 7
Window Size: 21, Training Step Size: 14
Window Size: 21, Training Step Size: 21
Window Size: 21, Training Step Size: 28
Window Size: 28, Training Step Size: 7
Window Size: 28, Training Step Size: 14
Window Size: 28, Training Step Size: 21
Window Size: 28, Training Step Size: 28

def evaluate_model_residues(model, test_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    with torch.no_grad():
        for X_batch, y_batch in test_loader:
            X_batch, y_batch = X_batch.to(device), y_batch.to(device)
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)
    
    # Concatenación y verificación de dimensiones
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)
    
    # Imprimir las longitudes para ver si coinciden
    print(f"Dimensiones de all_predictions: {all_predictions.shape}")
    print(f"Dimensiones de all_targets: {all_targets.shape}")
    
    # Verificar si las dimensiones coinciden antes de realizar operaciones
    if all_targets.shape != all_predictions.shape:
        raise ValueError(f"Dimensiones no coinciden: all_targets {all_targets.shape}, all_predictions {all_predictions.shape}")
    
    # Calcular residuos
    residues = all_targets - all_predictions
    
    # Calcular métricas
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (len(all_targets) - 1) / (len(all_targets) - window_size - 1)
    
    results_df = pd.DataFrame({
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })
    
    return residues, results_df

import os
import torch
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error, r2_score
from torch.utils.data import DataLoader

# Identificación del mejor modelo
model_with_max_r2_adj = mlp_result_df.loc[mlp_result_df['R² adj'].idxmax(), 'Model']
print(f"Model with the largest R² adjusted: {model_with_max_r2_adj}")

# Cargar el mejor modelo
checkpoint = torch.load(os.path.join(shared_folder_path, model_with_max_r2_adj))
input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

# Definir el modelo y cargar los parámetros
rnn_model = RNNModel(input_size, hidden_size, output_size, num_layers)
rnn_model.load_state_dict(checkpoint['state_dict'])
rnn_model.to(device)
print("Model loaded successfully!")

# Evaluación del modelo
def evaluate_model_residues(model, test_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    
    with torch.no_grad():
        for X_batch, y_batch in test_loader:
            X_batch, y_batch = X_batch.to(device), y_batch.to(device)
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)
    
    # Concatenar todas las predicciones y objetivos
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)
    
    # Asegurar que las longitudes coincidan
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]
    
    # Calcular residuos
    residues = all_targets - all_predictions
    
    # Calcular métricas
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (len(all_targets) - 1) / (len(all_targets) - input_size - 1)
    
    results_df = pd.DataFrame({
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })
    
    return residues, results_df

# Evaluación y visualización
residues, results_df = evaluate_model_residues(rnn_model, test_loader, criterion)
test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(rnn_model, test_loader, criterion, scaler, window_size, "RNN")

# Visualización de las predicciones y los valores reales
plt.plot(test_predictions.reshape(-1), label='Test Predictions')
plt.plot(test_targets.reshape(-1), label='Test Targets')
plt.legend()
plt.show()

# Mostrar el DataFrame con las métricas de evaluación
print(test_metrics_df)

Model with the largest R² adjusted: rnn_model_21_7.pth
Model loaded successfully!

  Model       MAPE      RMSE        R²    R² adj
0   RNN  24.971811  0.120363 -0.886196 -1.357746

import torch
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import statsmodels.api as sm
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error, r2_score
from scipy.stats import kurtosistest, skewtest, jarque_bera
from statsmodels.tsa.stattools import adfuller, kpss

def count_parameters(model):
    return sum(p.numel() for p in model.parameters() if p.requires_grad)

def calculate_adjusted_r2(all_targets, all_predictions, model):
    n = len(all_targets)
    k = count_parameters(model)  # Total number of trainable parameters

    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (n - 1) / (n - k - 1)

    print(f"R²: {r2:.4f}")
    print(f"R² adjusted: {r2_adj:.4f}")
    print(f"Number of trainable parameters: {k}")
    print(f"Number of measures: {n}")

    return r2_adj

def evaluate_model_residues(model, data_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    
    with torch.no_grad():
        for X_batch, y_batch in data_loader:
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)

    # Concatenate all predictions and targets
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)

    # Asegurarse de que las longitudes coincidan
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]

    residues = all_targets - all_predictions

    # Calculate statistics
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)

    kurt_stat, kurt_p_value = kurtosistest(residues)
    skew_stat, skew_p_value = skewtest(residues)
    jb_stat, jb_p_value = jarque_bera(residues)
    adf_stat, adf_p_value, _, _, _, _ = adfuller(residues)
    kpss_stat, kpss_p_value, _, _ = kpss(residues)

    results = {
        'MAPE': mape,
        'RMSE': rmse,
        'R²': r2,
        'Kurtosis (statistic)': kurt_stat,
        'Kurtosis (p-value)': kurt_p_value,
        'Skewness (statistic)': skew_stat,
        'Skewness (p-value)': skew_p_value,
        'Jarque-Bera (statistic)': jb_stat,
        'Jarque-Bera (p-value)': jb_p_value,
        'Dickey Fuller (statistic)': adf_stat,
        'Dickey Fuller (p-value)': adf_p_value,
        'KPSS test (statistic)': kpss_stat,
        'KPSS test (p-value)': kpss_p_value
    }

    results_df = pd.DataFrame.from_dict(results, orient='index', columns=['Value'])

    # Plotting the time series of residues
    plt.figure(figsize=(10, 6))
    plt.plot(residues)
    plt.title('Time Series of Residues')
    plt.xlabel('Time')
    plt.ylabel('Residues')
    plt.show()

    # Plotting the histogram of residues
    plt.figure(figsize=(10, 6))
    sns.histplot(residues, kde=True)
    plt.title('Histogram of Residues')
    plt.xlabel('Residues')
    plt.ylabel('Frequency')
    plt.show()

    # Q-Q plot of residues
    plt.figure(figsize=(10, 6))
    sm.qqplot(residues, line='s')
    plt.title('Q-Q Plot of Residues')
    plt.show()

    # ACF plot of residues
    plt.figure(figsize=(10, 6))
    sm.graphics.tsa.plot_acf(residues, lags=40)
    plt.title('Autocorrelation Function (ACF) of Residues')
    plt.show()

    return residues, results_df

# Uso de la función para evaluar el modelo RNN
residues, results_df = evaluate_model_residues(rnn_model, test_loader, criterion)
print(results_df)

# Calcular el R² ajustado
adjusted_r2 = calculate_adjusted_r2(test_targets, test_predictions, rnn_model)

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

                               Value
MAPE                        0.249718
RMSE                        0.120363
R²                         -0.886196
Kurtosis (statistic)        1.452483
Kurtosis (p-value)          0.146367
Skewness (statistic)       -3.511924
Skewness (p-value)          0.000445
Jarque-Bera (statistic)    15.616594
Jarque-Bera (p-value)       0.000406
Dickey Fuller (statistic)  -2.615550
Dickey Fuller (p-value)     0.089826
KPSS test (statistic)       0.626704
KPSS test (p-value)         0.020209
R²: -0.8862
R² adjusted: 2.3138
Number of trainable parameters: 341
Number of measures: 141

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
rnn_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for RNN Model")
plt.grid()
plt.show()

RNN At

import torch
import torch.nn as nn
import os
import itertools
import pandas as pd
from torch.utils.data import DataLoader, TensorDataset

shared_folder_path = "C:\\Users\\Maestriadatos\\Documents\\lizcanollerenaparcial\\docs"
files = os.listdir(shared_folder_path)
print(files)



def evaluate_and_create_row(model, loader, criterion, scaler, window_size, model_name):
    model.eval()
    all_predictions = []
    all_targets = []

    with torch.no_grad():
        for X_batch, y_batch in loader:
            outputs = model(X_batch)
            all_predictions.append(outputs.cpu().numpy())
            all_targets.append(y_batch.cpu().numpy())

    # Aplanar las listas de predicciones y etiquetas
    all_predictions = np.concatenate(all_predictions, axis=0).reshape(-1)
    all_targets = np.concatenate(all_targets, axis=0).reshape(-1)

    # Aseguramos que ambas listas tengan el mismo tamaño
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]

    # Calculamos las métricas
    n = len(all_targets)
    p = window_size
    mape, rmse, r2, r2_adj = calculate_metrics(all_targets, all_predictions, n, p)

    metrics_df = pd.DataFrame({
        'Model': [model_name],
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })

    return all_predictions, all_targets, metrics_df


# Definimos la clase de la RNN
class RNNModel(nn.Module):
    def __init__(self, input_size, hidden_size, output_size, num_layers=1):
        super(RNNModel, self).__init__()
        self.hidden_size = hidden_size
        self.num_layers = num_layers
        self.rnn = nn.RNN(input_size, hidden_size, num_layers, batch_first=True)
        self.fc = nn.Linear(hidden_size, output_size)

    def forward(self, x):
        h0 = torch.zeros(self.num_layers, x.size(0), self.hidden_size).to(x.device)
        out, _ = self.rnn(x, h0)
        out = self.fc(out[:, -1, :])  # Tomamos solo la última salida
        return out

# Configuración y parámetros
window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]
validation_steps = 14
test_steps = 14
columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']
rnn_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):
    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'rnn_modelAt_{window_size}_{train_steps}.pth'
    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        rnn_result_df = pd.concat([rnn_result_df, valid_metrics_df], ignore_index=True)
        continue

    # Preparamos las ventanas de datos
    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_At_tensor, window_size, train_steps, validation_steps, test_steps)
    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)

    # Configuración del DataLoader
    batch_size = 1
    train_loader = DataLoader(TensorDataset(Xtrains, ytrains), batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(TensorDataset(Xvalids, yvalids), batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(TensorDataset(Xtests, ytests), batch_size=batch_size, shuffle=False)

    # Parámetros de la RNN
    input_size = window_size
    hidden_size = 10
    output_size = 1
    num_layers = 1

    # Definimos el modelo
    model = RNNModel(input_size, hidden_size, output_size, num_layers).to(device)
    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=0.01)

    # Entrenamiento de la RNN
    num_epochs = 100
    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()
            optimizer.step()
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    # Guardado del modelo
    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)
    rnn_result_df = pd.concat([rnn_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df,
        'state_dict': model.state_dict()
    }, os.path.join(shared_folder_path, model_name))

['.git', 'bitcoinhistoricaldata.csv', 'intro.md', 'logo.png', 'lstm_modelAt_14_14.pth', 'lstm_modelAt_14_21.pth', 'lstm_modelAt_14_28.pth', 'lstm_modelAt_14_7.pth', 'lstm_modelAt_21_14.pth', 'lstm_modelAt_21_21.pth', 'lstm_modelAt_21_28.pth', 'lstm_modelAt_21_7.pth', 'lstm_modelAt_28_14.pth', 'lstm_modelAt_28_21.pth', 'lstm_modelAt_28_28.pth', 'lstm_modelAt_28_7.pth', 'lstm_modelAt_7_14.pth', 'lstm_modelAt_7_21.pth', 'lstm_modelAt_7_28.pth', 'lstm_modelAt_7_7.pth', 'lstm_modelVol7_14_14.pth', 'lstm_modelVol7_14_21.pth', 'lstm_modelVol7_14_28.pth', 'lstm_modelVol7_14_7.pth', 'lstm_modelVol7_21_14.pth', 'lstm_modelVol7_21_21.pth', 'lstm_modelVol7_21_28.pth', 'lstm_modelVol7_21_7.pth', 'lstm_modelVol7_28_14.pth', 'lstm_modelVol7_28_21.pth', 'lstm_modelVol7_28_28.pth', 'lstm_modelVol7_28_7.pth', 'lstm_modelVol7_7_14.pth', 'lstm_modelVol7_7_21.pth', 'lstm_modelVol7_7_28.pth', 'lstm_modelVol7_7_7.pth', 'lstm_model_14_14.pth', 'lstm_model_14_21.pth', 'lstm_model_14_28.pth', 'lstm_model_14_7.pth', 'lstm_model_21_14.pth', 'lstm_model_21_21.pth', 'lstm_model_21_28.pth', 'lstm_model_21_7.pth', 'lstm_model_28_14.pth', 'lstm_model_28_21.pth', 'lstm_model_28_28.pth', 'lstm_model_28_7.pth', 'lstm_model_7_14.pth', 'lstm_model_7_21.pth', 'lstm_model_7_28.pth', 'lstm_model_7_7.pth', 'markdown-notebooks.md', 'markdown.md', 'mlp_model_14_14.pth', 'mlp_model_14_21.pth', 'mlp_model_14_28.pth', 'mlp_model_14_7.pth', 'mlp_model_21_14.pth', 'mlp_model_21_21.pth', 'mlp_model_21_28.pth', 'mlp_model_21_7.pth', 'mlp_model_28_14.pth', 'mlp_model_28_21.pth', 'mlp_model_28_28.pth', 'mlp_model_28_7.pth', 'mlp_model_7_14.pth', 'mlp_model_7_21.pth', 'mlp_model_7_28.pth', 'mlp_model_7_7.pth', 'notebooks.ipynb', 'references.bib', 'requirements.txt', 'rnn_modelAt_14_14.pth', 'rnn_modelAt_14_21.pth', 'rnn_modelAt_14_28.pth', 'rnn_modelAt_14_7.pth', 'rnn_modelAt_21_14.pth', 'rnn_modelAt_21_21.pth', 'rnn_modelAt_21_28.pth', 'rnn_modelAt_21_7.pth', 'rnn_modelAt_28_14.pth', 'rnn_modelAt_28_21.pth', 'rnn_modelAt_28_28.pth', 'rnn_modelAt_28_7.pth', 'rnn_modelAt_7_14.pth', 'rnn_modelAt_7_21.pth', 'rnn_modelAt_7_28.pth', 'rnn_modelAt_7_7.pth', 'rnn_modelVol_14_14.pth', 'rnn_modelVol_14_21.pth', 'rnn_modelVol_14_28.pth', 'rnn_modelVol_14_7.pth', 'rnn_modelVol_21_14.pth', 'rnn_modelVol_21_21.pth', 'rnn_modelVol_21_28.pth', 'rnn_modelVol_21_7.pth', 'rnn_modelVol_28_14.pth', 'rnn_modelVol_28_21.pth', 'rnn_modelVol_28_28.pth', 'rnn_modelVol_28_7.pth', 'rnn_modelVol_7_14.pth', 'rnn_modelVol_7_21.pth', 'rnn_modelVol_7_28.pth', 'rnn_modelVol_7_7.pth', 'rnn_model_14_14.pth', 'rnn_model_14_21.pth', 'rnn_model_14_28.pth', 'rnn_model_14_7.pth', 'rnn_model_21_14.pth', 'rnn_model_21_21.pth', 'rnn_model_21_28.pth', 'rnn_model_21_7.pth', 'rnn_model_28_14.pth', 'rnn_model_28_21.pth', 'rnn_model_28_28.pth', 'rnn_model_28_7.pth', 'rnn_model_7_14.pth', 'rnn_model_7_21.pth', 'rnn_model_7_28.pth', 'rnn_model_7_7.pth', '_build', '_config.yml', '_toc.yml']
Device: cpu
Window Size: 7, Training Step Size: 7
Window Size: 7, Training Step Size: 14
Window Size: 7, Training Step Size: 21
Window Size: 7, Training Step Size: 28
Window Size: 14, Training Step Size: 7
Window Size: 14, Training Step Size: 14
Window Size: 14, Training Step Size: 21
Window Size: 14, Training Step Size: 28
Window Size: 21, Training Step Size: 7
Window Size: 21, Training Step Size: 14
Window Size: 21, Training Step Size: 21
Window Size: 21, Training Step Size: 28
Window Size: 28, Training Step Size: 7
Window Size: 28, Training Step Size: 14
Window Size: 28, Training Step Size: 21
Window Size: 28, Training Step Size: 28

def evaluate_model_residues(model, test_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    with torch.no_grad():
        for X_batch, y_batch in test_loader:
            X_batch, y_batch = X_batch.to(device), y_batch.to(device)
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)
    
    # Concatenación y verificación de dimensiones
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)
    
    # Imprimir las longitudes para ver si coinciden
    print(f"Dimensiones de all_predictions: {all_predictions.shape}")
    print(f"Dimensiones de all_targets: {all_targets.shape}")
    
    # Verificar si las dimensiones coinciden antes de realizar operaciones
    if all_targets.shape != all_predictions.shape:
        raise ValueError(f"Dimensiones no coinciden: all_targets {all_targets.shape}, all_predictions {all_predictions.shape}")
    
    # Calcular residuos
    residues = all_targets - all_predictions
    
    # Calcular métricas
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (len(all_targets) - 1) / (len(all_targets) - window_size - 1)
    
    results_df = pd.DataFrame({
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })
    
    return residues, results_df

import os
import torch
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error, r2_score
from torch.utils.data import DataLoader

mlp_result_df_filtered = mlp_result_df.dropna(subset=['R² adj'])
if mlp_result_df_filtered.empty:
    raise ValueError("No hay modelos con valores válidos de 'R² adj'.")
else:
    model_with_max_r2_adj = mlp_result_df_filtered.loc[mlp_result_df_filtered['R² adj'].idxmax(), 'Model']
    print(f"Model with the largest R² adjusted: {model_with_max_r2_adj}")


# Cargar el mejor modelo
checkpoint = torch.load(os.path.join(shared_folder_path, model_with_max_r2_adj))
input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

# Definir el modelo y cargar los parámetros
rnn_model = RNNModel(input_size, hidden_size, output_size, num_layers)
rnn_model.load_state_dict(checkpoint['state_dict'])
rnn_model.to(device)
print("Model loaded successfully!")

# Evaluación del modelo
def evaluate_model_residues(model, test_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    
    with torch.no_grad():
        for X_batch, y_batch in test_loader:
            X_batch, y_batch = X_batch.to(device), y_batch.to(device)
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)
    
    # Concatenar todas las predicciones y objetivos
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)
    
    # Asegurar que las longitudes coincidan
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]
    
    # Calcular residuos
    residues = all_targets - all_predictions
    
    # Calcular métricas
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (len(all_targets) - 1) / (len(all_targets) - input_size - 1)
    
    results_df = pd.DataFrame({
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })
    
    return residues, results_df

# Evaluación y visualización
residues, results_df = evaluate_model_residues(rnn_model, test_loader, criterion)
test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(rnn_model, test_loader, criterion, scaler, window_size, "RNN")

# Visualización de las predicciones y los valores reales
plt.plot(test_predictions.reshape(-1), label='Test Predictions')
plt.plot(test_targets.reshape(-1), label='Test Targets')
plt.legend()
plt.show()

# Mostrar el DataFrame con las métricas de evaluación
print(test_metrics_df)

Model with the largest R² adjusted: rnn_model_21_7.pth
Model loaded successfully!

  Model       MAPE      RMSE        R²    R² adj
0   RNN  24.971811  0.120363 -0.886196 -1.357746

import torch
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import statsmodels.api as sm
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error, r2_score
from scipy.stats import kurtosistest, skewtest, jarque_bera
from statsmodels.tsa.stattools import adfuller, kpss

def count_parameters(model):
    return sum(p.numel() for p in model.parameters() if p.requires_grad)

def calculate_adjusted_r2(all_targets, all_predictions, model):
    n = len(all_targets)
    k = count_parameters(model)  # Total number of trainable parameters

    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (n - 1) / (n - k - 1)

    print(f"R²: {r2:.4f}")
    print(f"R² adjusted: {r2_adj:.4f}")
    print(f"Number of trainable parameters: {k}")
    print(f"Number of measures: {n}")

    return r2_adj

def evaluate_model_residues(model, data_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    
    with torch.no_grad():
        for X_batch, y_batch in data_loader:
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)

    # Concatenate all predictions and targets
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)

    # Asegurarse de que las longitudes coincidan
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]

    residues = all_targets - all_predictions

    # Calculate statistics
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)

    kurt_stat, kurt_p_value = kurtosistest(residues)
    skew_stat, skew_p_value = skewtest(residues)
    jb_stat, jb_p_value = jarque_bera(residues)
    adf_stat, adf_p_value, _, _, _, _ = adfuller(residues)
    kpss_stat, kpss_p_value, _, _ = kpss(residues)

    results = {
        'MAPE': mape,
        'RMSE': rmse,
        'R²': r2,
        'Kurtosis (statistic)': kurt_stat,
        'Kurtosis (p-value)': kurt_p_value,
        'Skewness (statistic)': skew_stat,
        'Skewness (p-value)': skew_p_value,
        'Jarque-Bera (statistic)': jb_stat,
        'Jarque-Bera (p-value)': jb_p_value,
        'Dickey Fuller (statistic)': adf_stat,
        'Dickey Fuller (p-value)': adf_p_value,
        'KPSS test (statistic)': kpss_stat,
        'KPSS test (p-value)': kpss_p_value
    }

    results_df = pd.DataFrame.from_dict(results, orient='index', columns=['Value'])

    # Plotting the time series of residues
    plt.figure(figsize=(10, 6))
    plt.plot(residues)
    plt.title('Time Series of Residues')
    plt.xlabel('Time')
    plt.ylabel('Residues')
    plt.show()

    # Plotting the histogram of residues
    plt.figure(figsize=(10, 6))
    sns.histplot(residues, kde=True)
    plt.title('Histogram of Residues')
    plt.xlabel('Residues')
    plt.ylabel('Frequency')
    plt.show()

    # Q-Q plot of residues
    plt.figure(figsize=(10, 6))
    sm.qqplot(residues, line='s')
    plt.title('Q-Q Plot of Residues')
    plt.show()

    # ACF plot of residues
    plt.figure(figsize=(10, 6))
    sm.graphics.tsa.plot_acf(residues, lags=40)
    plt.title('Autocorrelation Function (ACF) of Residues')
    plt.show()

    return residues, results_df

# Uso de la función para evaluar el modelo RNN
residues, results_df = evaluate_model_residues(rnn_model, test_loader, criterion)
print(results_df)

# Calcular el R² ajustado
adjusted_r2 = calculate_adjusted_r2(test_targets, test_predictions, rnn_model)

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

                               Value
MAPE                        0.249718
RMSE                        0.120363
R²                         -0.886196
Kurtosis (statistic)        1.452483
Kurtosis (p-value)          0.146367
Skewness (statistic)       -3.511924
Skewness (p-value)          0.000445
Jarque-Bera (statistic)    15.616594
Jarque-Bera (p-value)       0.000406
Dickey Fuller (statistic)  -2.615550
Dickey Fuller (p-value)     0.089826
KPSS test (statistic)       0.626704
KPSS test (p-value)         0.020209
R²: -0.8862
R² adjusted: 2.3138
Number of trainable parameters: 341
Number of measures: 141

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
lstm_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for RNN Model")
plt.grid()
plt.show()

RNN Volatilidad

import torch
import torch.nn as nn
import os
import itertools
import pandas as pd
from torch.utils.data import DataLoader, TensorDataset

shared_folder_path = "C:\\Users\\Maestriadatos\\Documents\\lizcanollerenaparcial\\docs"
files = os.listdir(shared_folder_path)
print(files)



def evaluate_and_create_row(model, loader, criterion, scaler, window_size, model_name):
    model.eval()
    all_predictions = []
    all_targets = []

    with torch.no_grad():
        for X_batch, y_batch in loader:
            outputs = model(X_batch)
            all_predictions.append(outputs.cpu().numpy())
            all_targets.append(y_batch.cpu().numpy())

    # Aplanar las listas de predicciones y etiquetas
    all_predictions = np.concatenate(all_predictions, axis=0).reshape(-1)
    all_targets = np.concatenate(all_targets, axis=0).reshape(-1)

    # Aseguramos que ambas listas tengan el mismo tamaño
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]

    # Calculamos las métricas
    n = len(all_targets)
    p = window_size
    mape, rmse, r2, r2_adj = calculate_metrics(all_targets, all_predictions, n, p)

    metrics_df = pd.DataFrame({
        'Model': [model_name],
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })

    return all_predictions, all_targets, metrics_df


# Definimos la clase de la RNN
class RNNModel(nn.Module):
    def __init__(self, input_size, hidden_size, output_size, num_layers=1):
        super(RNNModel, self).__init__()
        self.hidden_size = hidden_size
        self.num_layers = num_layers
        self.rnn = nn.RNN(input_size, hidden_size, num_layers, batch_first=True)
        self.fc = nn.Linear(hidden_size, output_size)

    def forward(self, x):
        h0 = torch.zeros(self.num_layers, x.size(0), self.hidden_size).to(x.device)
        out, _ = self.rnn(x, h0)
        out = self.fc(out[:, -1, :])  # Tomamos solo la última salida
        return out

# Configuración y parámetros
window_sizes = [7, 14, 21, 28]
training_step_sizes = [7, 14, 21, 28]
validation_steps = 14
test_steps = 14
columns = ['Model', 'MAPE', 'RMSE', 'R²', 'R² adj']
rnn_result_df = pd.DataFrame(columns=columns)

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
print(f'Device: {device}')

for window_size, train_steps in itertools.product(window_sizes, training_step_sizes):
    print(f'Window Size: {window_size}, Training Step Size: {train_steps}')

    model_name = f'rnn_modelVol_{window_size}_{train_steps}.pth'
    if os.path.exists(os.path.join(shared_folder_path, model_name)):
        checkpoint = torch.load(os.path.join(shared_folder_path, model_name))
        valid_metrics_df = checkpoint['valid_metrics_df']
        rnn_result_df = pd.concat([rnn_result_df, valid_metrics_df], ignore_index=True)
        continue

    # Preparamos las ventanas de datos
    Xtrains, ytrains, Xvalids, yvalids, Xtests, ytests = create_windows(btc_Vol_tensor, window_size, train_steps, validation_steps, test_steps)
    Xtrains = torch.tensor(Xtrains, dtype=torch.float32).view(-1, train_steps, window_size).to(device)
    ytrains = torch.tensor(ytrains, dtype=torch.float32).view(-1, train_steps, 1).to(device)
    Xvalids = torch.tensor(Xvalids, dtype=torch.float32).view(-1, validation_steps, window_size).to(device)
    yvalids = torch.tensor(yvalids, dtype=torch.float32).view(-1, validation_steps, 1).to(device)
    Xtests = torch.tensor(Xtests, dtype=torch.float32).view(-1, test_steps, window_size).to(device)
    ytests = torch.tensor(ytests, dtype=torch.float32).view(-1, test_steps, 1).to(device)

    # Configuración del DataLoader
    batch_size = 1
    train_loader = DataLoader(TensorDataset(Xtrains, ytrains), batch_size=batch_size, shuffle=True)
    valid_loader = DataLoader(TensorDataset(Xvalids, yvalids), batch_size=batch_size, shuffle=False)
    test_loader = DataLoader(TensorDataset(Xtests, ytests), batch_size=batch_size, shuffle=False)

    # Parámetros de la RNN
    input_size = window_size
    hidden_size = 10
    output_size = 1
    num_layers = 1

    # Definimos el modelo
    model = RNNModel(input_size, hidden_size, output_size, num_layers).to(device)
    criterion = nn.MSELoss()
    optimizer = torch.optim.Adam(model.parameters(), lr=0.01)

    # Entrenamiento de la RNN
    num_epochs = 50
    for epoch in range(num_epochs):
        model.train()
        epoch_loss = 0
        for X_batch, y_batch in train_loader:
            optimizer.zero_grad()
            outputs = model(X_batch)
            loss = criterion(outputs, y_batch)
            loss.backward()
            optimizer.step()
            epoch_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            avg_loss = epoch_loss / len(train_loader)
            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {avg_loss:.4f}')

    # Guardado del modelo
    _, _, valid_metrics_df = evaluate_and_create_row(model, valid_loader, criterion, scaler, window_size, model_name)
    rnn_result_df = pd.concat([rnn_result_df, valid_metrics_df], ignore_index=True)

    torch.save({
        'input_size': input_size,
        'hidden_size': hidden_size,
        'output_size': output_size,
        'num_layers': num_layers,
        'test_loader': test_loader,
        'valid_metrics_df': valid_metrics_df,
        'state_dict': model.state_dict()
    }, os.path.join(shared_folder_path, model_name))

['.git', 'bitcoinhistoricaldata.csv', 'intro.md', 'logo.png', 'lstm_modelAt_14_14.pth', 'lstm_modelAt_14_21.pth', 'lstm_modelAt_14_28.pth', 'lstm_modelAt_14_7.pth', 'lstm_modelAt_21_14.pth', 'lstm_modelAt_21_21.pth', 'lstm_modelAt_21_28.pth', 'lstm_modelAt_21_7.pth', 'lstm_modelAt_28_14.pth', 'lstm_modelAt_28_21.pth', 'lstm_modelAt_28_28.pth', 'lstm_modelAt_28_7.pth', 'lstm_modelAt_7_14.pth', 'lstm_modelAt_7_21.pth', 'lstm_modelAt_7_28.pth', 'lstm_modelAt_7_7.pth', 'lstm_modelVol7_14_14.pth', 'lstm_modelVol7_14_21.pth', 'lstm_modelVol7_14_28.pth', 'lstm_modelVol7_14_7.pth', 'lstm_modelVol7_21_14.pth', 'lstm_modelVol7_21_21.pth', 'lstm_modelVol7_21_28.pth', 'lstm_modelVol7_21_7.pth', 'lstm_modelVol7_28_14.pth', 'lstm_modelVol7_28_21.pth', 'lstm_modelVol7_28_28.pth', 'lstm_modelVol7_28_7.pth', 'lstm_modelVol7_7_14.pth', 'lstm_modelVol7_7_21.pth', 'lstm_modelVol7_7_28.pth', 'lstm_modelVol7_7_7.pth', 'lstm_model_14_14.pth', 'lstm_model_14_21.pth', 'lstm_model_14_28.pth', 'lstm_model_14_7.pth', 'lstm_model_21_14.pth', 'lstm_model_21_21.pth', 'lstm_model_21_28.pth', 'lstm_model_21_7.pth', 'lstm_model_28_14.pth', 'lstm_model_28_21.pth', 'lstm_model_28_28.pth', 'lstm_model_28_7.pth', 'lstm_model_7_14.pth', 'lstm_model_7_21.pth', 'lstm_model_7_28.pth', 'lstm_model_7_7.pth', 'markdown-notebooks.md', 'markdown.md', 'mlp_model_14_14.pth', 'mlp_model_14_21.pth', 'mlp_model_14_28.pth', 'mlp_model_14_7.pth', 'mlp_model_21_14.pth', 'mlp_model_21_21.pth', 'mlp_model_21_28.pth', 'mlp_model_21_7.pth', 'mlp_model_28_14.pth', 'mlp_model_28_21.pth', 'mlp_model_28_28.pth', 'mlp_model_28_7.pth', 'mlp_model_7_14.pth', 'mlp_model_7_21.pth', 'mlp_model_7_28.pth', 'mlp_model_7_7.pth', 'notebooks.ipynb', 'references.bib', 'requirements.txt', 'rnn_modelAt_14_14.pth', 'rnn_modelAt_14_21.pth', 'rnn_modelAt_14_28.pth', 'rnn_modelAt_14_7.pth', 'rnn_modelAt_21_14.pth', 'rnn_modelAt_21_21.pth', 'rnn_modelAt_21_28.pth', 'rnn_modelAt_21_7.pth', 'rnn_modelAt_28_14.pth', 'rnn_modelAt_28_21.pth', 'rnn_modelAt_28_28.pth', 'rnn_modelAt_28_7.pth', 'rnn_modelAt_7_14.pth', 'rnn_modelAt_7_21.pth', 'rnn_modelAt_7_28.pth', 'rnn_modelAt_7_7.pth', 'rnn_modelVol_14_14.pth', 'rnn_modelVol_14_21.pth', 'rnn_modelVol_14_28.pth', 'rnn_modelVol_14_7.pth', 'rnn_modelVol_21_14.pth', 'rnn_modelVol_21_21.pth', 'rnn_modelVol_21_28.pth', 'rnn_modelVol_21_7.pth', 'rnn_modelVol_28_14.pth', 'rnn_modelVol_28_21.pth', 'rnn_modelVol_28_28.pth', 'rnn_modelVol_28_7.pth', 'rnn_modelVol_7_14.pth', 'rnn_modelVol_7_21.pth', 'rnn_modelVol_7_28.pth', 'rnn_modelVol_7_7.pth', 'rnn_model_14_14.pth', 'rnn_model_14_21.pth', 'rnn_model_14_28.pth', 'rnn_model_14_7.pth', 'rnn_model_21_14.pth', 'rnn_model_21_21.pth', 'rnn_model_21_28.pth', 'rnn_model_21_7.pth', 'rnn_model_28_14.pth', 'rnn_model_28_21.pth', 'rnn_model_28_28.pth', 'rnn_model_28_7.pth', 'rnn_model_7_14.pth', 'rnn_model_7_21.pth', 'rnn_model_7_28.pth', 'rnn_model_7_7.pth', '_build', '_config.yml', '_toc.yml']
Device: cpu
Window Size: 7, Training Step Size: 7
Window Size: 7, Training Step Size: 14
Window Size: 7, Training Step Size: 21
Window Size: 7, Training Step Size: 28
Window Size: 14, Training Step Size: 7
Window Size: 14, Training Step Size: 14
Window Size: 14, Training Step Size: 21
Window Size: 14, Training Step Size: 28
Window Size: 21, Training Step Size: 7
Window Size: 21, Training Step Size: 14
Window Size: 21, Training Step Size: 21
Window Size: 21, Training Step Size: 28
Window Size: 28, Training Step Size: 7
Window Size: 28, Training Step Size: 14
Window Size: 28, Training Step Size: 21
Window Size: 28, Training Step Size: 28

def evaluate_model_residues(model, test_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    with torch.no_grad():
        for X_batch, y_batch in test_loader:
            X_batch, y_batch = X_batch.to(device), y_batch.to(device)
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)
    
    # Concatenación y verificación de dimensiones
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)
    
    # Imprimir las longitudes para ver si coinciden
    print(f"Dimensiones de all_predictions: {all_predictions.shape}")
    print(f"Dimensiones de all_targets: {all_targets.shape}")
    
    # Verificar si las dimensiones coinciden antes de realizar operaciones
    if all_targets.shape != all_predictions.shape:
        raise ValueError(f"Dimensiones no coinciden: all_targets {all_targets.shape}, all_predictions {all_predictions.shape}")
    
    # Calcular residuos
    residues = all_targets - all_predictions
    
    # Calcular métricas
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (len(all_targets) - 1) / (len(all_targets) - window_size - 1)
    
    results_df = pd.DataFrame({
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })
    
    return residues, results_df

import os
import torch
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error, r2_score
from torch.utils.data import DataLoader

mlp_result_df_filtered = mlp_result_df.dropna(subset=['R² adj'])
if mlp_result_df_filtered.empty:
    raise ValueError("No hay modelos con valores válidos de 'R² adj'.")
else:
    model_with_max_r2_adj = mlp_result_df_filtered.loc[mlp_result_df_filtered['R² adj'].idxmax(), 'Model']
    print(f"Model with the largest R² adjusted: {model_with_max_r2_adj}")


# Cargar el mejor modelo
checkpoint = torch.load(os.path.join(shared_folder_path, model_with_max_r2_adj))
input_size = checkpoint['input_size']
hidden_size = checkpoint['hidden_size']
output_size = checkpoint['output_size']
num_layers = checkpoint['num_layers']
test_loader = checkpoint['test_loader']

# Definir el modelo y cargar los parámetros
rnn_model = RNNModel(input_size, hidden_size, output_size, num_layers)
rnn_model.load_state_dict(checkpoint['state_dict'])
rnn_model.to(device)
print("Model loaded successfully!")

# Evaluación del modelo
def evaluate_model_residues(model, test_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    
    with torch.no_grad():
        for X_batch, y_batch in test_loader:
            X_batch, y_batch = X_batch.to(device), y_batch.to(device)
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)
    
    # Concatenar todas las predicciones y objetivos
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)
    
    # Asegurar que las longitudes coincidan
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]
    
    # Calcular residuos
    residues = all_targets - all_predictions
    
    # Calcular métricas
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (len(all_targets) - 1) / (len(all_targets) - input_size - 1)
    
    results_df = pd.DataFrame({
        'MAPE': [mape],
        'RMSE': [rmse],
        'R²': [r2],
        'R² adj': [r2_adj]
    })
    
    return residues, results_df

# Evaluación y visualización
residues, results_df = evaluate_model_residues(rnn_model, test_loader, criterion)
test_predictions, test_targets, test_metrics_df = evaluate_and_create_row(rnn_model, test_loader, criterion, scaler, window_size, "RNN")

# Visualización de las predicciones y los valores reales
plt.plot(test_predictions.reshape(-1), label='Test Predictions')
plt.plot(test_targets.reshape(-1), label='Test Targets')
plt.legend()
plt.show()

# Mostrar el DataFrame con las métricas de evaluación
print(test_metrics_df)

Model with the largest R² adjusted: rnn_model_21_7.pth
Model loaded successfully!

  Model       MAPE      RMSE        R²    R² adj
0   RNN  24.971811  0.120363 -0.886196 -1.357746

import torch
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import statsmodels.api as sm
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error, r2_score
from scipy.stats import kurtosistest, skewtest, jarque_bera
from statsmodels.tsa.stattools import adfuller, kpss

def count_parameters(model):
    return sum(p.numel() for p in model.parameters() if p.requires_grad)

def calculate_adjusted_r2(all_targets, all_predictions, model):
    n = len(all_targets)
    k = count_parameters(model)  # Total number of trainable parameters

    r2 = r2_score(all_targets, all_predictions)
    r2_adj = 1 - (1 - r2) * (n - 1) / (n - k - 1)

    print(f"R²: {r2:.4f}")
    print(f"R² adjusted: {r2_adj:.4f}")
    print(f"Number of trainable parameters: {k}")
    print(f"Number of measures: {n}")

    return r2_adj

def evaluate_model_residues(model, data_loader, criterion):
    model.eval()
    all_predictions = []
    all_targets = []
    
    with torch.no_grad():
        for X_batch, y_batch in data_loader:
            outputs = model(X_batch)
            all_predictions.append(outputs)
            all_targets.append(y_batch)

    # Concatenate all predictions and targets
    all_predictions = torch.cat(all_predictions, dim=0).cpu().numpy().reshape(-1)
    all_targets = torch.cat(all_targets, dim=0).cpu().numpy().reshape(-1)

    # Asegurarse de que las longitudes coincidan
    min_length = min(len(all_targets), len(all_predictions))
    all_targets = all_targets[:min_length]
    all_predictions = all_predictions[:min_length]

    residues = all_targets - all_predictions

    # Calculate statistics
    mape = mean_absolute_percentage_error(all_targets, all_predictions)
    rmse = np.sqrt(mean_squared_error(all_targets, all_predictions))
    r2 = r2_score(all_targets, all_predictions)

    kurt_stat, kurt_p_value = kurtosistest(residues)
    skew_stat, skew_p_value = skewtest(residues)
    jb_stat, jb_p_value = jarque_bera(residues)
    adf_stat, adf_p_value, _, _, _, _ = adfuller(residues)
    kpss_stat, kpss_p_value, _, _ = kpss(residues)

    results = {
        'MAPE': mape,
        'RMSE': rmse,
        'R²': r2,
        'Kurtosis (statistic)': kurt_stat,
        'Kurtosis (p-value)': kurt_p_value,
        'Skewness (statistic)': skew_stat,
        'Skewness (p-value)': skew_p_value,
        'Jarque-Bera (statistic)': jb_stat,
        'Jarque-Bera (p-value)': jb_p_value,
        'Dickey Fuller (statistic)': adf_stat,
        'Dickey Fuller (p-value)': adf_p_value,
        'KPSS test (statistic)': kpss_stat,
        'KPSS test (p-value)': kpss_p_value
    }

    results_df = pd.DataFrame.from_dict(results, orient='index', columns=['Value'])

    # Plotting the time series of residues
    plt.figure(figsize=(10, 6))
    plt.plot(residues)
    plt.title('Time Series of Residues')
    plt.xlabel('Time')
    plt.ylabel('Residues')
    plt.show()

    # Plotting the histogram of residues
    plt.figure(figsize=(10, 6))
    sns.histplot(residues, kde=True)
    plt.title('Histogram of Residues')
    plt.xlabel('Residues')
    plt.ylabel('Frequency')
    plt.show()

    # Q-Q plot of residues
    plt.figure(figsize=(10, 6))
    sm.qqplot(residues, line='s')
    plt.title('Q-Q Plot of Residues')
    plt.show()

    # ACF plot of residues
    plt.figure(figsize=(10, 6))
    sm.graphics.tsa.plot_acf(residues, lags=40)
    plt.title('Autocorrelation Function (ACF) of Residues')
    plt.show()

    return residues, results_df

# Uso de la función para evaluar el modelo RNN
residues, results_df = evaluate_model_residues(rnn_model, test_loader, criterion)
print(results_df)

# Calcular el R² ajustado
adjusted_r2 = calculate_adjusted_r2(test_targets, test_predictions, rnn_model)

<Figure size 1000x600 with 0 Axes>

<Figure size 1000x600 with 0 Axes>

                               Value
MAPE                        0.249718
RMSE                        0.120363
R²                         -0.886196
Kurtosis (statistic)        1.452483
Kurtosis (p-value)          0.146367
Skewness (statistic)       -3.511924
Skewness (p-value)          0.000445
Jarque-Bera (statistic)    15.616594
Jarque-Bera (p-value)       0.000406
Dickey Fuller (statistic)  -2.615550
Dickey Fuller (p-value)     0.089826
KPSS test (statistic)       0.626704
KPSS test (p-value)         0.020209
R²: -0.8862
R² adjusted: 2.3138
Number of trainable parameters: 341
Number of measures: 141

import matplotlib.pyplot as plt
import pandas as pd

# Asegúrate de que 'lstm_result_df' contiene resultados de cada combinación de `window_size` y `train_steps`
# Añadimos una columna para numerar las corridas de entrenamiento
lstm_result_df['Run'] = range(1, len(lstm_result_df) + 1)

# Selecciona la métrica de los residuos que deseas graficar en el eje Y
# Aquí usaremos 'RMSE' como ejemplo; ajusta si prefieres otra métrica, como 'MAPE'
metric_to_plot = 'RMSE'

plt.figure(figsize=(10, 6))
plt.plot(lstm_result_df['Run'], lstm_result_df[metric_to_plot], marker='o', linestyle='-')
plt.xlabel("Run (Combination of Window Size and Training Step Size)")
plt.ylabel(f"{metric_to_plot} (Residual Score)")
plt.title(f"Error/Score vs Run for RNN Model")
plt.grid()
plt.show()